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 A286145 Square array read by antidiagonals: A(n,k) = T(n XOR k, k), where T(n,k) is sequence A001477 considered as a two-dimensional table, and XOR is bitwise-xor (A003987). 6
 0, 4, 2, 12, 1, 5, 24, 18, 13, 9, 40, 17, 3, 8, 14, 60, 50, 11, 7, 26, 20, 84, 49, 61, 6, 42, 19, 27, 112, 98, 85, 73, 62, 52, 43, 35, 144, 97, 59, 72, 10, 51, 25, 34, 44, 180, 162, 83, 71, 22, 16, 41, 33, 64, 54, 220, 161, 181, 70, 38, 15, 23, 32, 88, 53, 65, 264, 242, 221, 201, 58, 48, 39, 31, 116, 102, 89, 77, 312, 241, 179, 200, 222, 47, 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 MathWorld, Pairing Function FORMULA A(n,k) = T(A003987(n,k), 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,   4,  12,  24,  40,  60,  84, 112, 144, 180, 220, 264, 312    2,   1,  18,  17,  50,  49,  98,  97, 162, 161, 242, 241, 338    5,  13,   3,  11,  61,  85,  59,  83, 181, 221, 179, 219, 365    9,   8,   7,   6,  73,  72,  71,  70, 201, 200, 199, 198, 393   14,  26,  42,  62,  10,  22,  38,  58, 222, 266, 314, 366, 218   20,  19,  52,  51,  16,  15,  48,  47, 244, 243, 340, 339, 240   27,  43,  25,  41,  23,  39,  21,  37, 267, 315, 265, 313, 263   35,  34,  33,  32,  31,  30,  29,  28, 291, 290, 289, 288, 287   44,  64,  88, 116, 148, 184, 224, 268,  36,  56,  80, 108, 140   54,  53, 102, 101, 166, 165, 246, 245,  46,  45,  94,  93, 158   65,  89,  63,  87, 185, 225, 183, 223,  57,  81,  55,  79, 177   77,  76,  75,  74, 205, 204, 203, 202,  69,  68,  67,  66, 197   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], k]; Table[A[k, n - k ], {n, 0, 20}, {k, 0, n}] // Flatten (* Indranil Ghosh, May 21 2017 *) PROG (Scheme) (define (A286145 n) (A286145bi (A002262 n) (A025581 n))) (define (A286145bi row col) (let ((a (A003987bi row col)) (b col)) (/ (+ (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, k) for n in range(21): print([A(k, n - k) for k in range(n + 1)]) # Indranil Ghosh, May 21 2017 CROSSREFS Transpose: A286147. Cf. A046092 (row 0), A000096 (column 0), A000217 (main diagonal). Cf. A003987, A001477, A286108, A286109, A286150, A286151. Sequence in context: A094406 A142706 A092952 * A010318 A188134 A226725 Adjacent sequences:  A286142 A286143 A286144 * A286146 A286147 A286148 KEYWORD nonn,tabl AUTHOR Antti Karttunen, May 03 2017 STATUS approved

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Last modified July 28 09:36 EDT 2021. Contains 346325 sequences. (Running on oeis4.)