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 A286147 Square array read by antidiagonals: A(n,k) = T(n XOR k, n), where T(n,k) is sequence A001477 considered as a two-dimensional table, and XOR is bitwise-xor (A003987) 6
 0, 2, 4, 5, 1, 12, 9, 13, 18, 24, 14, 8, 3, 17, 40, 20, 26, 7, 11, 50, 60, 27, 19, 42, 6, 61, 49, 84, 35, 43, 52, 62, 73, 85, 98, 112, 44, 34, 25, 51, 10, 72, 59, 97, 144, 54, 64, 33, 41, 16, 22, 71, 83, 162, 180, 65, 53, 88, 32, 23, 15, 38, 70, 181, 161, 220, 77, 89, 102, 116, 31, 39, 48, 58, 201, 221, 242, 264, 90, 76, 63, 101, 148, 30, 21, 47, 222, 200, 179, 241, 312 (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), n), 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     4,   1,  13,   8,  26,  19,  43,  34,  64,  53,  89,  76, 118    12,  18,   3,   7,  42,  52,  25,  33,  88, 102,  63,  75, 150    24,  17,  11,   6,  62,  51,  41,  32, 116, 101,  87,  74, 186    40,  50,  61,  73,  10,  16,  23,  31, 148, 166, 185, 205,  86    60,  49,  85,  72,  22,  15,  39,  30, 184, 165, 225, 204, 114    84,  98,  59,  71,  38,  48,  21,  29, 224, 246, 183, 203, 146   112,  97,  83,  70,  58,  47,  37,  28, 268, 245, 223, 202, 182   144, 162, 181, 201, 222, 244, 267, 291,  36,  46,  57,  69,  82   180, 161, 221, 200, 266, 243, 315, 290,  56,  45,  81,  68, 110   220, 242, 179, 199, 314, 340, 265, 289,  80,  94,  55,  67, 142   264, 241, 219, 198, 366, 339, 313, 288, 108,  93,  79,  66, 178   312, 338, 365, 393, 218, 240, 263, 287, 140, 158, 177, 197,  78 MATHEMATICA T[a_, b_]:=((a + b)^2 + 3a + b)/2; A[n_, k_]:=T[BitXor[n, k], k]; Table[A[n - k, k], {n, 0, 20}, {k, 0, n}] // Flatten (* Indranil Ghosh, May 21 2017 *) PROG (Scheme) (define (A286147 n) (A286147bi (A002262 n) (A025581 n))) (define (A286147bi row col) (let ((a (A003987bi row col)) (b 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, k) for n in xrange(0, 21): print [A(n - k, k) for k in xrange(0, n + 1)] # Indranil Ghosh, May 21 2017 CROSSREFS Transpose: A286145. Cf. A000096 (row 0), A046092 (column 0), A000217 (main diagonal). Cf. A003987, A001477, A286108, A286109, A286150, A286151. Sequence in context: A274316 A075884 A030750 * A059215 A125142 A234350 Adjacent sequences:  A286144 A286145 A286146 * A286148 A286149 A286150 KEYWORD nonn,tabl AUTHOR Antti Karttunen, May 03 2017 STATUS approved

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Last modified June 16 06:46 EDT 2019. Contains 324145 sequences. (Running on oeis4.)