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 A286109 Square array read by antidiagonals: A(n,k) = T(n XOR k, 2*(n AND k)), where T(n,k) is sequence A001477 considered as a two-dimensional table, AND is bitwise-and (A004198) and XOR is bitwise-xor (A003987). 7
 0, 2, 2, 5, 3, 5, 9, 9, 9, 9, 14, 12, 10, 12, 14, 20, 20, 16, 16, 20, 20, 27, 25, 27, 21, 27, 25, 27, 35, 35, 35, 35, 35, 35, 35, 35, 44, 42, 40, 42, 36, 42, 40, 42, 44, 54, 54, 50, 50, 46, 46, 50, 50, 54, 54, 65, 63, 65, 59, 57, 55, 57, 59, 65, 63, 65, 77, 77, 77, 77, 69, 69, 69, 69, 77, 77, 77, 77, 90, 88, 86, 88, 90, 80, 78, 80, 90, 88, 86, 88, 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 Eric Weisstein's World of Mathematics, Pairing Function FORMULA A(n,k) = T(A003987(n,k), 2*A004198(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,   3,   9,  12,  20,  25,  35,  42,  54,  63,  77,  88, 104    5,   9,  10,  16,  27,  35,  40,  50,  65,  77,  86, 100, 119    9,  12,  16,  21,  35,  42,  50,  59,  77,  88, 100, 113, 135   14,  20,  27,  35,  36,  46,  57,  69,  90, 104, 119, 135, 144   20,  25,  35,  42,  46,  55,  69,  80, 104, 117, 135, 150, 162   27,  35,  40,  50,  57,  69,  78,  92, 119, 135, 148, 166, 181   35,  42,  50,  59,  69,  80,  92, 105, 135, 150, 166, 183, 201   44,  54,  65,  77,  90, 104, 119, 135, 136, 154, 173, 193, 214   54,  63,  77,  88, 104, 117, 135, 150, 154, 171, 193, 212, 236   65,  77,  86, 100, 119, 135, 148, 166, 173, 193, 210, 232, 259   77,  88, 100, 113, 135, 150, 166, 183, 193, 212, 232, 253, 283   90, 104, 119, 135, 144, 162, 181, 201, 214, 236, 259, 283, 300 MATHEMATICA T[a_, b_]:=((a + b)^2 + 3a + b)/2; A[n_, k_]:=T[BitXor[n, k], 2*BitAnd[n, k]]; Table[A[k, n - k ], {n, 0, 20}, {k, 0, n}] // Flatten (* Indranil Ghosh, May 20 2017 *) PROG (Scheme) (define (A286109 n) (A286109bi (A002262 n) (A025581 n))) (define (A286109bi row col) (let ((a (A003987bi row col)) (b (* 2 (A004198bi row col)))) (/ (+ (expt (+ a b) 2) (* 3 a) b) 2))) ;; Here A003987bi and A004198bi implement bitwise-xor (A003987) and bitwise-and (A004198). (Python) def T(a, b): return ((a + b)**2 + 3*a + b)/2 def A(n, k): return T(n^k, 2*(n&k)) for n in xrange(0, 21): print [A(k, n - k) for k in xrange(0, n + 1)] # Indranil Ghosh, May 20 2017 CROSSREFS Cf. A000096 (row 0 & column 0), A014105 (main diagonal). Cf. A003056, A003987, A004198. Cf. also arrays A286099, A286108, A286145, A286147, A286150, A286151. Sequence in context: A174608 A130327 A224361 * A239665 A178179 A284833 Adjacent sequences:  A286106 A286107 A286108 * A286110 A286111 A286112 KEYWORD nonn,tabl AUTHOR Antti Karttunen, May 03 2017 STATUS approved

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Last modified May 26 22:16 EDT 2019. Contains 323597 sequences. (Running on oeis4.)