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 A286150 Square array read by antidiagonals: A(n,k) = T(n XOR k, min(n,k)), where T(n,k) is sequence A001477 considered as a two-dimensional table, and XOR is bitwise-xor (A003987). 6
 0, 2, 2, 5, 1, 5, 9, 13, 13, 9, 14, 8, 3, 8, 14, 20, 26, 7, 7, 26, 20, 27, 19, 42, 6, 42, 19, 27, 35, 43, 52, 62, 62, 52, 43, 35, 44, 34, 25, 51, 10, 51, 25, 34, 44, 54, 64, 33, 41, 16, 16, 41, 33, 64, 54, 65, 53, 88, 32, 23, 15, 23, 32, 88, 53, 65, 77, 89, 102, 116, 31, 39, 39, 31, 116, 102, 89, 77, 90, 76, 63, 101, 148, 30, 21, 30, 148, 101, 63, 76, 90 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 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 A(n,k) = T(A003987(n,k), min(n,k)), where T(n,k) is sequence A001477 considered as a two-dimensional table, that is, as a pairing function from [0, 1, 2, 3, ...] x [0, 1, 2, 3, ...] to [0, 1, 2, 3, ...]. EXAMPLE The top left 0 .. 12 x 0 .. 12 corner of the array: 0, 2, 5, 9, 14, 20, 27, 35, 44, 54, 65, 77, 90 2, 1, 13, 8, 26, 19, 43, 34, 64, 53, 89, 76, 118 5, 13, 3, 7, 42, 52, 25, 33, 88, 102, 63, 75, 150 9, 8, 7, 6, 62, 51, 41, 32, 116, 101, 87, 74, 186 14, 26, 42, 62, 10, 16, 23, 31, 148, 166, 185, 205, 86 20, 19, 52, 51, 16, 15, 39, 30, 184, 165, 225, 204, 114 27, 43, 25, 41, 23, 39, 21, 29, 224, 246, 183, 203, 146 35, 34, 33, 32, 31, 30, 29, 28, 268, 245, 223, 202, 182 44, 64, 88, 116, 148, 184, 224, 268, 36, 46, 57, 69, 82 54, 53, 102, 101, 166, 165, 246, 245, 46, 45, 81, 68, 110 65, 89, 63, 87, 185, 225, 183, 223, 57, 81, 55, 67, 142 77, 76, 75, 74, 205, 204, 203, 202, 69, 68, 67, 66, 178 90, 118, 150, 186, 86, 114, 146, 182, 82, 110, 142, 178, 78 MATHEMATICA T[a_, b_]:=((a + b)^2 + 3a + b)/2; A[n_, k_]:=T[BitXor[n, k], Min[n, k]]; Table[A[k, n - k], {n, 0, 20}, {k, 0, n}] // Flatten (* Indranil Ghosh, May 21 2017 *) PROG (Scheme) (define (A286150 n) (A286150bi (A002262 n) (A025581 n))) (define (A286150bi row col) (let ((a (A003987bi row col)) (b (min col row))) (/ (+ (expt (+ a b) 2) (* 3 a) b) 2))) ;; 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, min(n, k)) for n in range(21): print([A(k, n - k) for k in range(n + 1)]) # Indranil Ghosh, May 21 2017 CROSSREFS Cf. A000096 (row 0 & column 0), A000217 (main diagonal). Cf. A003987, A001477, A286108, A286109, A286145, A286147, A286151. Sequence in context: A079301 A079300 A128932 * A071950 A274847 A165922 Adjacent sequences: A286147 A286148 A286149 * A286151 A286152 A286153 KEYWORD nonn,tabl AUTHOR Antti Karttunen, May 03 2017 STATUS approved

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Last modified September 21 18:26 EDT 2023. Contains 365503 sequences. (Running on oeis4.)