Examples of Solutions found by Simulated Annealing Hugo Pfoertner 2024-01-25 a(2) = 54 Trace(A) = 5 [1, 2; 3, 4] --------- a(3)= 761 Trace(A) = 14 [1, 3, 5; 2, 4, 8; 6, 7, 9] Trace(A) = 16 [1, 2, 5; 3, 6, 7; 4, 8, 9] ----------- a(4) = 5284 Trace(A) = 34 96 solutions with A(1,1)=1 and A(4,4)=16 found by exhaustive enumeration 1 2 5 8 3 4 9 11 6 10 13 14 7 12 15 16 1 2 5 8 3 4 9 12 6 10 13 14 7 11 15 16 1 2 5 8 3 4 10 11 6 9 13 14 7 12 15 16 1 2 5 8 3 4 10 11 6 9 13 15 7 12 14 16 1 2 5 10 3 4 7 11 6 8 13 14 9 12 15 16 1 2 5 10 3 4 7 12 6 8 13 14 9 11 15 16 1 2 5 10 3 4 8 11 6 7 13 14 9 12 15 16 1 2 5 10 3 4 8 11 6 7 13 15 9 12 14 16 1 2 6 7 3 4 9 11 5 10 13 15 8 12 14 16 1 2 6 7 3 4 9 12 5 10 13 14 8 11 15 16 1 2 6 7 3 4 9 12 5 10 13 15 8 11 14 16 1 2 6 7 3 4 10 11 5 9 13 15 8 12 14 16 1 2 6 8 3 4 9 11 5 10 13 14 7 12 15 16 1 2 6 8 3 4 9 11 5 10 13 15 7 12 14 16 1 2 6 8 3 4 9 12 5 10 13 14 7 11 15 16 1 2 6 8 3 4 10 11 5 9 13 15 7 12 14 16 1 2 6 9 3 4 7 11 5 8 13 15 10 12 14 16 1 2 6 9 3 4 7 12 5 8 13 14 10 11 15 16 1 2 6 9 3 4 7 12 5 8 13 15 10 11 14 16 1 2 6 9 3 4 8 11 5 7 13 15 10 12 14 16 1 2 6 10 3 4 7 11 5 8 13 14 9 12 15 16 1 2 6 10 3 4 7 11 5 8 13 15 9 12 14 16 1 2 6 10 3 4 7 12 5 8 13 14 9 11 15 16 1 2 6 10 3 4 8 11 5 7 13 15 9 12 14 16 1 3 5 7 2 4 9 12 6 10 13 14 8 11 15 16 1 3 5 7 2 4 10 11 6 9 13 15 8 12 14 16 1 3 5 7 2 4 10 12 6 9 13 14 8 11 15 16 1 3 5 7 2 4 10 12 6 9 13 15 8 11 14 16 1 3 5 8 2 4 9 12 6 10 13 14 7 11 15 16 1 3 5 8 2 4 10 11 6 9 13 14 7 12 15 16 1 3 5 8 2 4 10 11 6 9 13 15 7 12 14 16 1 3 5 8 2 4 10 12 6 9 13 14 7 11 15 16 1 3 5 9 2 4 7 12 6 8 13 14 10 11 15 16 1 3 5 9 2 4 8 11 6 7 13 15 10 12 14 16 1 3 5 9 2 4 8 12 6 7 13 14 10 11 15 16 1 3 5 9 2 4 8 12 6 7 13 15 10 11 14 16 1 3 5 10 2 4 7 12 6 8 13 14 9 11 15 16 1 3 5 10 2 4 8 11 6 7 13 14 9 12 15 16 1 3 5 10 2 4 8 11 6 7 13 15 9 12 14 16 1 3 5 10 2 4 8 12 6 7 13 14 9 11 15 16 1 3 6 7 2 4 9 12 5 10 13 14 8 11 15 16 1 3 6 7 2 4 9 12 5 10 13 15 8 11 14 16 1 3 6 7 2 4 10 11 5 9 13 15 8 12 14 16 1 3 6 7 2 4 10 12 5 9 13 15 8 11 14 16 1 3 6 9 2 4 7 12 5 8 13 14 10 11 15 16 1 3 6 9 2 4 7 12 5 8 13 15 10 11 14 16 1 3 6 9 2 4 8 11 5 7 13 15 10 12 14 16 1 3 6 9 2 4 8 12 5 7 13 15 10 11 14 16 1 5 2 8 6 13 9 14 3 10 4 11 7 15 12 16 1 5 2 8 6 13 9 15 3 10 4 11 7 14 12 16 1 5 2 8 6 13 10 14 3 9 4 11 7 15 12 16 1 5 2 8 6 13 10 14 3 9 4 12 7 15 11 16 1 5 2 10 6 13 7 14 3 8 4 11 9 15 12 16 1 5 2 10 6 13 7 15 3 8 4 11 9 14 12 16 1 5 2 10 6 13 8 14 3 7 4 11 9 15 12 16 1 5 2 10 6 13 8 14 3 7 4 12 9 15 11 16 1 5 3 7 6 13 9 14 2 10 4 12 8 15 11 16 1 5 3 7 6 13 9 15 2 10 4 11 8 14 12 16 1 5 3 7 6 13 9 15 2 10 4 12 8 14 11 16 1 5 3 7 6 13 10 14 2 9 4 12 8 15 11 16 1 5 3 8 6 13 9 14 2 10 4 11 7 15 12 16 1 5 3 8 6 13 9 14 2 10 4 12 7 15 11 16 1 5 3 8 6 13 9 15 2 10 4 11 7 14 12 16 1 5 3 8 6 13 10 14 2 9 4 12 7 15 11 16 1 5 3 9 6 13 7 14 2 8 4 12 10 15 11 16 1 5 3 9 6 13 7 15 2 8 4 11 10 14 12 16 1 5 3 9 6 13 7 15 2 8 4 12 10 14 11 16 1 5 3 9 6 13 8 14 2 7 4 12 10 15 11 16 1 5 3 10 6 13 7 14 2 8 4 11 9 15 12 16 1 5 3 10 6 13 7 14 2 8 4 12 9 15 11 16 1 5 3 10 6 13 7 15 2 8 4 11 9 14 12 16 1 5 3 10 6 13 8 14 2 7 4 12 9 15 11 16 1 6 2 7 5 13 9 15 3 10 4 11 8 14 12 16 1 6 2 7 5 13 10 14 3 9 4 12 8 15 11 16 1 6 2 7 5 13 10 15 3 9 4 11 8 14 12 16 1 6 2 7 5 13 10 15 3 9 4 12 8 14 11 16 1 6 2 8 5 13 9 15 3 10 4 11 7 14 12 16 1 6 2 8 5 13 10 14 3 9 4 11 7 15 12 16 1 6 2 8 5 13 10 14 3 9 4 12 7 15 11 16 1 6 2 8 5 13 10 15 3 9 4 11 7 14 12 16 1 6 2 9 5 13 7 15 3 8 4 11 10 14 12 16 1 6 2 9 5 13 8 14 3 7 4 12 10 15 11 16 1 6 2 9 5 13 8 15 3 7 4 11 10 14 12 16 1 6 2 9 5 13 8 15 3 7 4 12 10 14 11 16 1 6 2 10 5 13 7 15 3 8 4 11 9 14 12 16 1 6 2 10 5 13 8 14 3 7 4 11 9 15 12 16 1 6 2 10 5 13 8 14 3 7 4 12 9 15 11 16 1 6 2 10 5 13 8 15 3 7 4 11 9 14 12 16 1 6 3 7 5 13 9 15 2 10 4 11 8 14 12 16 1 6 3 7 5 13 9 15 2 10 4 12 8 14 11 16 1 6 3 7 5 13 10 14 2 9 4 12 8 15 11 16 1 6 3 7 5 13 10 15 2 9 4 12 8 14 11 16 1 6 3 9 5 13 7 15 2 8 4 11 10 14 12 16 1 6 3 9 5 13 7 15 2 8 4 12 10 14 11 16 1 6 3 9 5 13 8 14 2 7 4 12 10 15 11 16 1 6 3 9 5 13 8 15 2 7 4 12 10 14 11 16 ------------ a(5) = 24303 Trace(A) = 63: [ 1, 2, 5, 10, 13; 3, 4, 8, 14, 16; 6, 7, 11, 19, 20; 9, 15, 18, 22, 24; 12, 17, 21, 23, 25] Trace(A) = 65: [ 1, 2, 6, 10, 14; 3, 4, 7, 11, 17; 5, 8, 13, 19, 20; 9, 12, 18, 22, 24; 15, 16, 21, 23, 25] Trace(A) = 67: [1, 3, 5, 10, 11; 2, 4, 8, 14, 16; 6, 7, 15, 18, 21; 9, 13, 19, 22, 24; 12, 17, 20, 23, 25] ------------ a(6) = 85352 Trace(A) = 109: [ 1, 2, 5, 9, 15, 19; 3, 4, 8, 12, 21, 22; 6, 7, 11, 17, 25, 27; 10, 13, 16, 24, 29, 32; 14, 20, 26, 30, 33, 35; 18, 23, 28, 31, 34, 36] Trace(A) = 113: [ 1, 2, 6, 10, 14, 19; 3, 4, 7, 12, 17, 22; 5, 8, 13, 20, 25, 27; 9, 11, 21, 26, 30, 31; 15, 16, 24, 29, 33, 35; 18, 23, 28, 32, 34, 36] ------------- a(7) = 248045 Trace(A) = 174: [ 1, 3, 5, 11, 14, 21, 24; 2, 4, 8, 12, 19, 27, 29; 6, 7, 9, 16, 22, 32, 36; 10, 13, 17, 28, 34, 38, 40; 15, 18, 23, 33, 37, 42, 45; 20, 26, 31, 39, 43, 46, 48; 25, 30, 35, 41, 44, 47, 49] Trace(A) = 176: [ 1, 2, 5, 10, 15, 21, 23; 3, 4, 8, 12, 18, 25, 29; 6, 7, 13, 17, 27, 31, 36; 9, 11, 16, 22, 34, 38, 40; 14, 19, 28, 33, 41, 43, 44; 20, 26, 32, 37, 42, 46, 48; 24, 30, 35, 39, 45, 47, 49] ------------- a(8) = 626610 Trace(A) = 258: [ 1, 3, 5, 10, 14, 22, 28, 31; 2, 4, 7, 12, 18, 26, 34, 37; 6, 8, 13, 16, 23, 36, 40, 45; 9, 11, 17, 20, 29, 42, 47, 51; 15, 19, 24, 30, 39, 48, 52, 54; 21, 25, 35, 43, 49, 56, 57, 60; 27, 33, 41, 46, 53, 58, 61, 63; 32, 38, 44, 50, 55, 59, 62, 64] Trace(A) = 260: [ 1, 2, 5, 9, 15, 22, 28, 32; 3, 4, 8, 12, 18, 25, 33, 37; 6, 7, 13, 16, 23, 36, 40, 45; 10, 11, 17, 20, 30, 42, 46, 48; 14, 19, 24, 29, 41, 51, 52, 54; 21, 26, 35, 43, 50, 56, 57, 60; 27, 34, 39, 47, 53, 58, 61, 62; 31, 38, 44, 49, 55, 59, 63, 64] Trace(A) = 262: [ 1, 2, 6, 11, 15, 20, 27, 31; 3, 4, 8, 12, 18, 25, 33, 38; 5, 7, 9, 16, 23, 30, 40, 44; 10, 13, 17, 26, 35, 42, 47, 50; 14, 19, 22, 36, 45, 48, 54, 55; 21, 24, 29, 41, 49, 52, 57, 60; 28, 34, 39, 46, 53, 58, 61, 62; 32, 37, 43, 51, 56, 59, 63, 64] -------------- a(9) = 1421271 Trace(A) = 365: [ 1, 2, 5, 11, 14, 24, 28, 35, 41; 3, 4, 7, 13, 19, 25, 34, 42, 46; 6, 8, 9, 16, 21, 31, 37, 49, 52; 10, 12, 17, 22, 30, 44, 51, 57, 60; 15, 18, 20, 29, 39, 55, 59, 64, 65; 23, 26, 32, 45, 54, 62, 67, 70, 73; 27, 33, 38, 50, 58, 68, 69, 75, 77; 36, 43, 48, 56, 63, 71, 74, 78, 80; 40, 47, 53, 61, 66, 72, 76, 79, 81] Trace(A) = 373: [ 1, 2, 6, 10, 17, 21, 29, 35, 42; 3, 4, 8, 11, 18, 26, 34, 39, 46; 5, 7, 13, 15, 23, 32, 44, 49, 55; 9, 12, 14, 20, 28, 37, 51, 57, 58; 16, 19, 24, 27, 43, 52, 62, 63, 68; 22, 25, 31, 38, 53, 60, 65, 69, 72; 30, 33, 45, 50, 61, 66, 73, 75, 76; 36, 40, 48, 56, 64, 70, 74, 78, 79; 41, 47, 54, 59, 67, 71, 77, 80, 81] --------------- a(10) = 2959798 Trace(A) = 501: [ 1, 3, 5, 10, 14, 24, 32, 36, 45, 50; 2, 4, 8, 12, 18, 26, 35, 43, 52, 56; 6, 7, 9, 17, 21, 29, 40, 47, 58, 63; 11, 13, 16, 22, 27, 38, 55, 60, 68, 71; 15, 19, 20, 28, 33, 49, 64, 69, 76, 77; 23, 25, 30, 39, 48, 66, 74, 80, 82, 84; 31, 34, 41, 54, 65, 73, 81, 87, 90, 92; 37, 42, 46, 61, 70, 79, 86, 88, 93, 96; 44, 53, 59, 67, 75, 83, 89, 94, 97, 99; 51, 57, 62, 72, 78, 85, 91, 95, 98, 100] Trace(A) = 503: [ 1, 2, 6, 10, 16, 23, 30, 40, 45, 52; 3, 4, 8, 11, 19, 25, 34, 43, 48, 56; 5, 7, 13, 14, 22, 32, 39, 54, 59, 65; 9, 12, 15, 20, 27, 36, 47, 63, 67, 69; 17, 18, 21, 28, 35, 51, 60, 72, 75, 78; 24, 26, 31, 37, 50, 66, 74, 80, 82, 87; 29, 33, 38, 46, 61, 73, 77, 85, 89, 91; 41, 42, 55, 62, 71, 81, 84, 92, 94, 97; 44, 49, 58, 68, 76, 83, 88, 93, 95, 98; 53, 57, 64, 70, 79, 86, 90, 96, 99, 100] Trace(A) = 507: [ 1, 2, 4, 11, 15, 23, 32, 37, 44, 48; 3, 6, 8, 12, 18, 25, 34, 42, 53, 57; 5, 7, 9, 16, 20, 30, 39, 46, 59, 60; 10, 13, 17, 24, 27, 40, 55, 62, 68, 71; 14, 19, 21, 28, 35, 51, 64, 69, 75, 78; 22, 26, 29, 41, 50, 66, 73, 80, 82, 85; 31, 33, 38, 54, 65, 74, 81, 87, 89, 92; 36, 43, 47, 63, 70, 79, 86, 88, 94, 95; 45, 52, 58, 67, 76, 83, 90, 93, 97, 98; 49, 56, 61, 72, 77, 84, 91, 96, 99, 100] Trace(A) = 509: [ 1, 3, 4, 10, 15, 22, 32, 37, 44, 48; 2, 6, 8, 13, 18, 26, 34, 43, 52, 56; 5, 7, 9, 17, 20, 30, 38, 46, 59, 60; 11, 12, 16, 24, 28, 40, 55, 63, 67, 71; 14, 19, 21, 27, 35, 51, 64, 69, 76, 78; 23, 25, 29, 41, 50, 66, 73, 80, 83, 85; 31, 33, 39, 54, 65, 74, 81, 86, 89, 92; 36, 42, 47, 62, 70, 79, 87, 90, 94, 96; 45, 53, 58, 68, 75, 82, 88, 93, 97, 99; 49, 57, 61, 72, 77, 84, 91, 95, 98, 100] --------------- a(11) = 5750977 Trace(A) = 664: [ 1, 2, 5, 10, 16, 22, 31, 39, 49, 56, 59; 3, 4, 7, 12, 20, 25, 35, 43, 52, 62, 67; 6, 8, 13, 15, 23, 29, 40, 51, 64, 71, 77; 9, 11, 14, 18, 28, 34, 47, 57, 70, 79, 82; 17, 19, 24, 27, 37, 45, 65, 75, 86, 88, 93; 21, 26, 30, 33, 44, 54, 73, 84, 91, 96, 99; 32, 36, 41, 46, 66, 74, 87, 94, 101, 103, 107; 38, 42, 50, 58, 76, 83, 95, 100, 105, 110, 113; 48, 53, 63, 69, 85, 90, 102, 106, 111, 115, 117; 55, 61, 72, 80, 89, 97, 104, 109, 114, 118, 119; 60, 68, 78, 81, 92, 98, 108, 112, 116, 120, 121] Trace(A) = 666: [ 1, 2, 5, 10, 17, 22, 32, 41, 46, 55, 61; 3, 4, 7, 12, 19, 25, 33, 42, 53, 60, 68; 6, 8, 9, 14, 23, 27, 38, 51, 58, 69, 74; 11, 13, 15, 20, 29, 36, 49, 63, 71, 79, 81; 16, 18, 24, 30, 37, 44, 65, 77, 84, 89, 93; 21, 26, 28, 35, 45, 56, 75, 85, 91, 94, 99; 31, 34, 39, 48, 66, 76, 87, 97, 100, 103, 105; 40, 43, 50, 64, 78, 86, 96, 102, 107, 110, 112; 47, 52, 57, 72, 83, 90, 101, 108, 111, 115, 116; 54, 59, 70, 80, 88, 95, 104, 109, 114, 118, 120; 62, 67, 73, 82, 92, 98, 106, 113, 117, 119, 121] Trace(A) = 676: [ 1, 2, 6, 9, 14, 24, 30, 40, 48, 55, 61; 3, 4, 8, 12, 18, 28, 34, 42, 52, 63, 67; 5, 7, 11, 17, 22, 31, 38, 51, 65, 70, 75; 10, 13, 16, 20, 25, 36, 45, 58, 72, 80, 81; 15, 19, 21, 26, 35, 46, 56, 74, 84, 88, 90; 23, 27, 32, 37, 47, 66, 77, 87, 94, 96, 101; 29, 33, 39, 44, 57, 78, 85, 92, 99, 104, 105; 41, 43, 50, 59, 73, 86, 93, 102, 107, 109, 112; 49, 53, 64, 71, 83, 95, 98, 108, 113, 114, 117; 54, 62, 69, 79, 89, 97, 103, 110, 115, 118, 120; 60, 68, 76, 82, 91, 100, 106, 111, 116, 119, 121] Trace(A) = 678: [ 1, 2, 5, 10, 15, 24, 29, 40, 44, 55, 61; 3, 4, 7, 13, 18, 25, 34, 43, 50, 62, 67; 6, 8, 11, 17, 20, 32, 36, 52, 58, 69, 74; 9, 12, 16, 22, 27, 38, 47, 65, 72, 80, 84; 14, 19, 21, 28, 35, 48, 56, 76, 82, 86, 90; 23, 26, 31, 39, 49, 68, 77, 89, 93, 96, 100; 30, 33, 37, 46, 57, 78, 85, 94, 99, 102, 105; 41, 42, 53, 64, 75, 88, 95, 104, 107, 111, 113; 45, 51, 59, 71, 81, 92, 98, 108, 109, 115, 116; 54, 63, 70, 79, 87, 97, 103, 110, 114, 118, 119; 60, 66, 73, 83, 91, 101, 106, 112, 117, 120, 121] ---------------- a(12) = 10550950 Trace(A) = 866: [ 1, 3, 6, 9, 16, 22, 31, 40, 49, 62, 65, 71; 2, 4, 8, 13, 19, 26, 34, 44, 53, 63, 74, 79; 5, 7, 11, 15, 24, 29, 39, 51, 60, 76, 81, 86; 10, 12, 14, 18, 28, 35, 43, 57, 67, 83, 93, 95; 17, 20, 23, 27, 37, 47, 55, 78, 88, 98, 102, 105; 21, 25, 30, 36, 46, 54, 70, 91, 96, 106, 111, 114; 32, 33, 38, 42, 56, 69, 85, 101, 109, 115, 120, 121; 41, 45, 50, 58, 77, 90, 100, 112, 117, 125, 126, 131; 48, 52, 59, 68, 89, 97, 108, 118, 123, 129, 133, 134; 61, 64, 75, 84, 99, 107, 116, 124, 128, 136, 137, 139; 66, 73, 82, 92, 103, 110, 119, 127, 132, 138, 141, 143; 72, 80, 87, 94, 104, 113, 122, 130, 135, 140, 142, 144] Trace(A) = 868: [ 1, 2, 6, 10, 17, 21, 31, 41, 48, 61, 66, 72; 3, 4, 7, 13, 19, 25, 33, 44, 52, 64, 74, 80; 5, 8, 11, 14, 24, 29, 39, 51, 59, 76, 81, 85; 9, 12, 15, 18, 28, 35, 43, 58, 68, 83, 92, 95; 16, 20, 23, 27, 37, 46, 55, 78, 89, 99, 103, 104; 22, 26, 30, 36, 47, 54, 69, 90, 96, 107, 110, 113; 32, 34, 38, 42, 56, 70, 87, 100, 109, 115, 119, 121; 40, 45, 50, 57, 77, 91, 101, 112, 118, 125, 127, 130; 49, 53, 60, 67, 88, 97, 108, 117, 123, 128, 133, 134; 62, 63, 75, 84, 98, 106, 116, 124, 129, 136, 138, 140; 65, 73, 82, 93, 102, 111, 120, 126, 132, 137, 141, 143; 71, 79, 86, 94, 105, 114, 122, 131, 135, 139, 142, 144] Trace(A) = 872: [ 1, 2, 6, 10, 15, 23, 32, 40, 51, 60, 65, 74; 3, 4, 7, 12, 18, 25, 34, 43, 52, 64, 72, 80; 5, 8, 9, 16, 21, 29, 39, 46, 61, 70, 82, 84; 11, 13, 17, 22, 27, 37, 48, 57, 77, 86, 92, 96; 14, 19, 20, 28, 33, 44, 54, 68, 88, 94, 100, 105; 24, 26, 30, 36, 45, 58, 75, 89, 102, 106, 112, 113; 31, 35, 38, 49, 55, 76, 91, 98, 109, 115, 120, 123; 41, 42, 47, 56, 67, 90, 99, 108, 118, 121, 125, 129; 50, 53, 62, 78, 87, 103, 110, 117, 127, 130, 133, 135; 59, 63, 69, 85, 95, 107, 116, 122, 131, 134, 138, 139; 66, 71, 81, 93, 101, 111, 119, 126, 132, 137, 141, 143; 73, 79, 83, 97, 104, 114, 124, 128, 136, 140, 142, 144] Trace(A) = 874: [ 1, 3, 6, 10, 15, 23, 32, 40, 51, 59, 65, 73; 2, 4, 8, 12, 18, 26, 34, 43, 53, 63, 71, 80; 5, 7, 9, 17, 20, 29, 39, 46, 61, 70, 82, 84; 11, 13, 16, 22, 27, 37, 48, 57, 77, 86, 92, 96; 14, 19, 21, 28, 33, 44, 55, 68, 87, 95, 100, 104; 24, 25, 30, 36, 45, 60, 75, 89, 103, 106, 112, 114; 31, 35, 38, 49, 54, 76, 91, 99, 110, 115, 120, 123; 41, 42, 47, 56, 67, 90, 98, 108, 118, 122, 125, 128; 50, 52, 62, 78, 88, 102, 109, 117, 127, 131, 133, 135; 58, 64, 69, 85, 94, 107, 116, 121, 130, 134, 138, 140; 66, 72, 81, 93, 101, 111, 119, 126, 132, 137, 141, 143; 74, 79, 83, 97, 105, 113, 124, 129, 136, 139, 142, 144] --------------- a(13) = 1844625 Trace(A) = 1109: [ 1, 2, 6, 10, 17, 23, 31, 41, 48, 62, 71, 77, 84; 3, 4, 8, 12, 18, 28, 35, 46, 53, 63, 75, 87, 92; 5, 7, 11, 14, 22, 30, 38, 51, 59, 74, 89, 94, 101; 9, 13, 15, 20, 26, 36, 45, 58, 65, 81, 96, 105, 108; 16, 19, 21, 25, 33, 43, 55, 70, 79, 99, 110, 116, 119; 24, 27, 29, 37, 42, 56, 68, 90, 102, 115, 122, 128, 129; 32, 34, 39, 44, 54, 67, 85, 106, 113, 124, 131, 137, 139; 40, 47, 50, 57, 69, 91, 107, 120, 126, 134, 143, 145, 148; 49, 52, 60, 66, 80, 103, 112, 125, 133, 140, 146, 151, 154; 61, 64, 73, 82, 98, 114, 123, 135, 141, 150, 156, 158, 159; 72, 76, 88, 97, 111, 121, 132, 142, 147, 155, 161, 162, 164; 78, 86, 95, 104, 117, 127, 136, 144, 152, 157, 163, 166, 168; 83, 93, 100, 109, 118, 130, 138, 149, 153, 160, 165, 167, 169] [ 1, 2, 6, 9, 17, 23, 31, 41, 49, 62, 71, 78, 83; 3, 4, 8, 13, 18, 28, 34, 46, 53, 64, 75, 86, 92; 5, 7, 11, 14, 21, 30, 39, 51, 60, 74, 88, 94, 101; 10, 12, 15, 20, 26, 37, 44, 58, 65, 81, 97, 104, 108; 16, 19, 22, 25, 33, 43, 54, 69, 80, 98, 110, 117, 119; 24, 27, 29, 36, 42, 56, 68, 91, 102, 115, 122, 127, 130; 32, 35, 38, 45, 55, 67, 85, 106, 112, 123, 131, 137, 139; 40, 47, 50, 57, 70, 90, 107, 120, 126, 134, 143, 145, 148; 48, 52, 59, 66, 79, 103, 113, 125, 133, 141, 147, 152, 153; 61, 63, 73, 82, 99, 114, 124, 135, 140, 150, 156, 157, 160; 72, 76, 89, 96, 111, 121, 132, 142, 146, 155, 161, 162, 165; 77, 87, 95, 105, 116, 128, 136, 144, 151, 158, 163, 166, 167; 84, 93, 100, 109, 118, 129, 138, 149, 154, 159, 164, 168, 169] ---------------- a(14) = 30942890 Trace(A) = 1371: [ 1, 3, 6, 11, 14, 24, 33, 40, 52, 62, 73, 84, 93, 100; 2, 4, 7, 13, 18, 28, 35, 45, 55, 65, 77, 89, 98, 106; 5, 8, 9, 17, 20, 29, 38, 49, 60, 69, 86, 97, 108, 113; 10, 12, 16, 22, 26, 37, 46, 57, 72, 82, 103, 115, 122, 126; 15, 19, 21, 25, 31, 43, 50, 63, 79, 91, 110, 123, 128, 133; 23, 27, 30, 36, 42, 54, 67, 81, 104, 117, 131, 138, 144, 147; 32, 34, 39, 47, 51, 68, 75, 95, 119, 129, 140, 148, 152, 156; 41, 44, 48, 58, 64, 80, 94, 118, 135, 142, 151, 158, 161, 166; 53, 56, 59, 71, 78, 105, 120, 136, 145, 155, 163, 168, 171, 175; 61, 66, 70, 83, 90, 116, 130, 141, 154, 160, 169, 174, 179, 180; 74, 76, 87, 102, 111, 132, 139, 150, 164, 170, 177, 182, 184, 188; 85, 88, 96, 114, 124, 137, 149, 159, 167, 173, 183, 186, 190, 192; 92, 99, 109, 121, 127, 143, 153, 162, 172, 178, 185, 189, 193, 195; 101, 107, 112, 125, 134, 146, 157, 165, 176, 181, 187, 191, 194, 196] Trace(A) = 1375: [ 1, 2, 5, 11, 14, 23, 32, 41, 53, 60, 73, 85, 93, 99; 3, 4, 7, 12, 19, 28, 34, 45, 57, 65, 76, 88, 101, 107; 6, 8, 9, 17, 21, 30, 38, 48, 61, 70, 87, 97, 108, 112; 10, 13, 16, 22, 25, 37, 47, 55, 72, 82, 103, 115, 121, 125; 15, 18, 20, 26, 31, 43, 51, 63, 80, 91, 111, 124, 129, 133; 24, 27, 29, 36, 42, 54, 68, 78, 105, 117, 132, 138, 143, 146; 33, 35, 39, 46, 50, 67, 75, 95, 119, 127, 140, 147, 153, 156; 40, 44, 49, 56, 64, 79, 94, 118, 135, 141, 150, 159, 162, 166; 52, 58, 62, 71, 81, 104, 120, 136, 149, 154, 163, 169, 172, 175; 59, 66, 69, 83, 90, 116, 128, 142, 155, 160, 168, 173, 178, 180; 74, 77, 86, 102, 110, 131, 139, 151, 164, 167, 177, 183, 185, 188; 84, 89, 96, 114, 123, 137, 148, 158, 170, 174, 182, 186, 190, 192; 92, 100, 109, 122, 130, 144, 152, 161, 171, 179, 184, 189, 193, 195; 98, 106, 113, 126, 134, 145, 157, 165, 176, 181, 187, 191, 194, 196] Trace(A) = 1383: [ 1, 2, 6, 10, 17, 21, 32, 40, 51, 64, 71, 84, 90, 99; 3, 4, 8, 12, 18, 26, 35, 45, 53, 67, 75, 89, 97, 105; 5, 7, 11, 15, 24, 28, 38, 50, 60, 73, 83, 100, 108, 112; 9, 13, 14, 20, 29, 34, 47, 57, 66, 87, 95, 110, 120, 123; 16, 19, 23, 30, 37, 42, 55, 70, 81, 106, 114, 128, 132, 138; 22, 25, 27, 33, 43, 48, 61, 78, 92, 116, 126, 136, 140, 145; 31, 36, 39, 46, 56, 62, 79, 103, 118, 134, 141, 149, 152, 156; 41, 44, 49, 58, 69, 77, 102, 122, 130, 147, 151, 158, 163, 164; 52, 54, 59, 65, 80, 93, 119, 129, 143, 154, 161, 168, 169, 174; 63, 68, 74, 86, 107, 117, 133, 146, 155, 166, 171, 176, 179, 182; 72, 76, 82, 94, 115, 125, 142, 150, 160, 172, 175, 181, 184, 187; 85, 88, 101, 111, 127, 135, 148, 159, 167, 177, 180, 188, 190, 192; 91, 96, 109, 121, 131, 139, 153, 162, 170, 178, 185, 189, 193, 194; 98, 104, 113, 124, 137, 144, 157, 165, 173, 183, 186, 191, 195, 196] Trace(A) = 1387: [ 1, 3, 6, 9, 17, 22, 31, 41, 50, 63, 72, 84, 90, 97; 2, 4, 7, 13, 19, 25, 35, 45, 53, 70, 76, 88, 98, 105; 5, 8, 11, 14, 23, 30, 39, 49, 60, 73, 82, 101, 109, 112; 10, 12, 15, 20, 28, 33, 47, 57, 65, 87, 94, 110, 121, 123; 16, 18, 24, 27, 37, 43, 55, 67, 81, 107, 114, 127, 132, 136; 21, 26, 29, 34, 42, 52, 62, 78, 93, 118, 125, 138, 141, 145; 32, 36, 38, 46, 56, 61, 79, 103, 117, 133, 140, 148, 152, 156; 40, 44, 48, 58, 68, 77, 102, 122, 130, 147, 151, 159, 163, 164; 51, 54, 59, 66, 80, 92, 116, 129, 143, 155, 160, 168, 170, 173; 64, 69, 74, 86, 106, 119, 134, 146, 154, 166, 172, 176, 179, 183; 71, 75, 83, 95, 115, 126, 139, 150, 161, 171, 175, 180, 184, 187; 85, 89, 100, 111, 128, 137, 149, 158, 167, 177, 181, 188, 189, 191; 91, 99, 108, 120, 131, 142, 153, 162, 169, 178, 185, 190, 193, 194; 96, 104, 113, 124, 135, 144, 157, 165, 174, 182, 186, 192, 195, 196]