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 A286108 Square array read by antidiagonals: A(n,k) = T(2*(n AND k), n XOR 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, 1, 1, 3, 5, 3, 6, 6, 6, 6, 10, 12, 14, 12, 10, 15, 15, 19, 19, 15, 15, 21, 23, 21, 27, 21, 23, 21, 28, 28, 28, 28, 28, 28, 28, 28, 36, 38, 40, 38, 44, 38, 40, 38, 36, 45, 45, 49, 49, 53, 53, 49, 49, 45, 45, 55, 57, 55, 61, 63, 65, 63, 61, 55, 57, 55, 66, 66, 66, 66, 74, 74, 74, 74, 66, 66, 66, 66, 78, 80, 82, 80, 78, 88, 90, 88, 78, 80, 82, 80, 78 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 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(2*A004198(n,k), A003987(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,  1,   3,   6,  10,  15,  21,  28,  36,  45,  55,  66,  78    1,  5,   6,  12,  15,  23,  28,  38,  45,  57,  66,  80,  91    3,  6,  14,  19,  21,  28,  40,  49,  55,  66,  82,  95, 105    6, 12,  19,  27,  28,  38,  49,  61,  66,  80,  95, 111, 120   10, 15,  21,  28,  44,  53,  63,  74,  78,  91, 105, 120, 144   15, 23,  28,  38,  53,  65,  74,  88,  91, 107, 120, 138, 161   21, 28,  40,  49,  63,  74,  90, 103, 105, 120, 140, 157, 179   28, 38,  49,  61,  74,  88, 103, 119, 120, 138, 157, 177, 198   36, 45,  55,  66,  78,  91, 105, 120, 152, 169, 187, 206, 226   45, 57,  66,  80,  91, 107, 120, 138, 169, 189, 206, 228, 247   55, 66,  82,  95, 105, 120, 140, 157, 187, 206, 230, 251, 269   66, 80,  95, 111, 120, 138, 157, 177, 206, 228, 251, 275, 292   78, 91, 105, 120, 144, 161, 179, 198, 226, 247, 269, 292, 324 MATHEMATICA T[a_, b_]:=((a + b)^2 + 3a + b)/2; A[n_, k_]:=T[2*BitAnd[n, k], BitXor[n, k]]; Table[A[k, n - k ], {n, 0, 20}, {k, 0, n}] // Flatten (* Indranil Ghosh, May 20 2017 *) PROG (Scheme) (define (A286108 n) (A286108bi (A002262 n) (A025581 n))) (define (A286108bi row col) (let ((a (* 2 (A004198bi row col))) (b (A003987bi 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(2*(n&k), 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. A000217 (row 0 & column 0), A014106 (main diagonal). Cf. A003056, A003987, A004198. Cf. also arrays A286098, A286109, A286145, A286147, A286150, A286151. Sequence in context: A151568 A134429 A100667 * A096438 A299418 A214456 Adjacent sequences:  A286105 A286106 A286107 * A286109 A286110 A286111 KEYWORD nonn,tabl AUTHOR Antti Karttunen, May 03 2017 STATUS approved

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Last modified May 19 06:57 EDT 2019. Contains 323386 sequences. (Running on oeis4.)