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 A286153 Square array read by descending antidiagonals A(1,1), A(1,2), A(2,1), ...: If n > k, A(n,k) = T(n XOR k, k), and otherwise A(n,k) = T(n, n XOR k), where T(n,k) is sequence A001477 considered as a two-dimensional table, and XOR is bitwise-xor (A003987). 5
 2, 11, 13, 7, 5, 8, 22, 8, 7, 26, 16, 38, 9, 42, 19, 37, 47, 58, 62, 52, 43, 29, 23, 48, 14, 51, 25, 34, 56, 30, 39, 19, 16, 41, 33, 64, 46, 80, 31, 25, 20, 23, 32, 88, 53, 79, 93, 108, 32, 41, 39, 31, 116, 102, 89, 67, 57, 94, 140, 33, 27, 30, 148, 101, 63, 76, 106, 68, 81, 157, 176, 34, 29, 184, 166, 87, 75, 118, 92, 138, 69, 175, 158, 216, 35, 224, 165, 185, 74, 150, 103 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS FORMULA A(n,k) = A286151(n,k), for n >= 1, k >= 1. If n > k, A(n,k) = T(A003987(n,k),k), otherwise A(n,k) = T(n,A003987(n,k)), where T(n,k) is sequence A001477 considered as a two-dimensional table, and XOR is bitwise-xor (A003987). EXAMPLE The top left 1 .. 12 x 1 .. 12 corner of the array:     2,  11,   7,  22,  16,  37,  29,  56,  46,  79,  67, 106    13,   5,   8,  38,  47,  23,  30,  80,  93,  57,  68, 138     8,   7,   9,  58,  48,  39,  31, 108,  94,  81,  69, 174    26,  42,  62,  14,  19,  25,  32, 140, 157, 175, 194,  82    19,  52,  51,  16,  20,  41,  33, 176, 158, 215, 195, 110    43,  25,  41,  23,  39,  27,  34, 216, 237, 177, 196, 142    34,  33,  32,  31,  30,  29,  35, 260, 238, 217, 197, 178    64,  88, 116, 148, 184, 224, 268,  44,  53,  63,  74,  86    53, 102, 101, 166, 165, 246, 245,  46,  54,  87,  75, 114    89,  63,  87, 185, 225, 183, 223,  57,  81,  65,  76, 146    76,  75,  74, 205, 204, 203, 202,  69,  68,  67,  77, 182   118, 150, 186,  86, 114, 146, 182,  82, 110, 142, 178,  90 MATHEMATICA T[a_, b_]:=((a + b)^2 + 3a + b)/2; A[n_, k_]:=If[n>k, T[BitXor[n, k], k], T[n, BitXor[n, k]]]; Table[A[k, n - k + 1], {n, 20}, {k, n}] // Flatten (* Indranil Ghosh, May 21 2017 *) PROG (Scheme) (define (A286153 n) (A286151bi (A002260 n) (A004736 n))) ;; For A286151bi see A286151. (Python) def T(a, b): return ((a + b)**2 + 3*a + b)/2 def A(n, k): return T(n^k, k) if n>k else T(n, n^k) for n in range(1, 21): print [A(k, n - k + 1) for k in range(1, n + 1)] # Indranil Ghosh, May 21 2017 CROSSREFS Array A286151 without its topmost row and leftmost column. Cf. A003987, A091255, A286155. Sequence in context: A037091 A289675 A127303 * A068972 A116437 A048867 Adjacent sequences:  A286150 A286151 A286152 * A286154 A286155 A286156 KEYWORD nonn,tabl AUTHOR Antti Karttunen, May 03 2017 STATUS approved

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Last modified August 8 23:02 EDT 2020. Contains 336300 sequences. (Running on oeis4.)