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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 MathWorld, 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 xrange(0, 21): print [A(k, n - k) for k in xrange(0, 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 June 17 22:17 EDT 2019. Contains 324200 sequences. (Running on oeis4.)