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 A286151 Square array read by descending antidiagonals: 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). 8
 0, 1, 2, 3, 2, 5, 6, 11, 13, 9, 10, 7, 5, 8, 14, 15, 22, 8, 7, 26, 20, 21, 16, 38, 9, 42, 19, 27, 28, 37, 47, 58, 62, 52, 43, 35, 36, 29, 23, 48, 14, 51, 25, 34, 44, 45, 56, 30, 39, 19, 16, 41, 33, 64, 54, 55, 46, 80, 31, 25, 20, 23, 32, 88, 53, 65, 66, 79, 93, 108, 32, 41, 39, 31, 116, 102, 89, 77, 78, 67, 57, 94, 140, 33, 27, 30, 148, 101, 63, 76, 90 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The array is read by descending antidiagonals as A(0,0), A(0,1), A(1,0), A(0,2), A(1,1), A(2,0), ... LINKS Antti Karttunen, Table of n, a(n) for n = 0..10584; the first 145 antidiagonals of array Eric Weisstein's World of Mathematics, Pairing Function FORMULA 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 0 .. 12 x 0 .. 12 corner of the array: 0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78 2, 2, 11, 7, 22, 16, 37, 29, 56, 46, 79, 67, 106 5, 13, 5, 8, 38, 47, 23, 30, 80, 93, 57, 68, 138 9, 8, 7, 9, 58, 48, 39, 31, 108, 94, 81, 69, 174 14, 26, 42, 62, 14, 19, 25, 32, 140, 157, 175, 194, 82 20, 19, 52, 51, 16, 20, 41, 33, 176, 158, 215, 195, 110 27, 43, 25, 41, 23, 39, 27, 34, 216, 237, 177, 196, 142 35, 34, 33, 32, 31, 30, 29, 35, 260, 238, 217, 197, 178 44, 64, 88, 116, 148, 184, 224, 268, 44, 53, 63, 74, 86 54, 53, 102, 101, 166, 165, 246, 245, 46, 54, 87, 75, 114 65, 89, 63, 87, 185, 225, 183, 223, 57, 81, 65, 76, 146 77, 76, 75, 74, 205, 204, 203, 202, 69, 68, 67, 77, 182 90, 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 ], {n, 0, 20}, {k, 0, n}] // Flatten (* Indranil Ghosh, May 20 2017 *) PROG (Scheme) (define (A286151 n) (A286151bi (A002262 n) (A025581 n))) (define (A286151bi row col) (define (pairA001477bi a b) (/ (+ (expt (+ a b) 2) (* 3 a) b) 2)) (cond ((> row col) (pairA001477bi (A003987bi row col) col)) (else (pairA001477bi row (A003987bi col row))))) ;; Where A003987bi implements bitwise-xor (A003987). (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(21): print([A(k, n - k) for k in range(n + 1)]) # Indranil Ghosh, May 20 2017 CROSSREFS Cf. A000217 (row 0), A000096 (column 0 and the main diagonal). Cf. A001477, A003987, A286108, A286109, A286145, A286147, A286150. Cf. A286153 (same array without row 0 and column 0). Sequence in context: A182880 A182898 A133684 * A192138 A175264 A025473 Adjacent sequences: A286148 A286149 A286150 * A286152 A286153 A286154 KEYWORD nonn,tabl AUTHOR Antti Karttunen, May 03 2017 STATUS approved

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Last modified February 22 22:43 EST 2024. Contains 370265 sequences. (Running on oeis4.)