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 A286099 Square array read by antidiagonals: A(n,k) = T(n OR k, n AND k), where T(n,k) is sequence A001477 considered as a two-dimensional table, AND is bitwise-and (A004198) and OR is bitwise-or (A003986). 5
 0, 2, 2, 5, 4, 5, 9, 9, 9, 9, 14, 13, 12, 13, 14, 20, 20, 18, 18, 20, 20, 27, 26, 27, 24, 27, 26, 27, 35, 35, 35, 35, 35, 35, 35, 35, 44, 43, 42, 43, 40, 43, 42, 43, 44, 54, 54, 52, 52, 50, 50, 52, 52, 54, 54, 65, 64, 65, 62, 61, 60, 61, 62, 65, 64, 65, 77, 77, 77, 77, 73, 73, 73, 73, 77, 77, 77, 77, 90, 89, 88, 89, 90, 85, 84, 85, 90, 89, 88, 89, 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(A003986(n,k), 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,   4,   9,  13,  20,  26,  35,  43,  54,  64,  77,  89, 104    5,   9,  12,  18,  27,  35,  42,  52,  65,  77,  88, 102, 119    9,  13,  18,  24,  35,  43,  52,  62,  77,  89, 102, 116, 135   14,  20,  27,  35,  40,  50,  61,  73,  90, 104, 119, 135, 148   20,  26,  35,  43,  50,  60,  73,  85, 104, 118, 135, 151, 166   27,  35,  42,  52,  61,  73,  84,  98, 119, 135, 150, 168, 185   35,  43,  52,  62,  73,  85,  98, 112, 135, 151, 168, 186, 205   44,  54,  65,  77,  90, 104, 119, 135, 144, 162, 181, 201, 222   54,  64,  77,  89, 104, 118, 135, 151, 162, 180, 201, 221, 244   65,  77,  88, 102, 119, 135, 150, 168, 181, 201, 220, 242, 267   77,  89, 102, 116, 135, 151, 168, 186, 201, 221, 242, 264, 291   90, 104, 119, 135, 148, 166, 185, 205, 222, 244, 267, 291, 312 MATHEMATICA T[a_, b_]:=((a + b)^2 + 3a + b)/2; A[n_, k_]:=T[BitOr[n, k], BitAnd[n,  k]]; Table[A[n - k, k], {n, 0, 20}, {k, 0, n}] // Flatten (* Indranil Ghosh, May 21 2017 *) PROG (Scheme) (define (A286099 n) (A286099bi (A002262 n) (A025581 n))) (define (A286099bi row col) (let ((a (A003986bi row col)) (b (A004198bi row col))) (/ (+ (expt (+ a b) 2) (* 3 a) b) 2))) ;; Here A003986bi and A004198bi implement bitwise-OR (A003986) 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, 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), A162761 (seems to be row 1 & column 1), A046092 (main diagonal). Cf. A003056, A003986, A004198. Cf. also arrays A286098, A286101, A286102, A286109. Sequence in context: A292245 A206427 A112923 * A098366 A284127 A261114 Adjacent sequences:  A286096 A286097 A286098 * A286100 A286101 A286102 KEYWORD nonn,tabl AUTHOR Antti Karttunen, May 03 2017 STATUS approved

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Last modified June 16 14:56 EDT 2019. Contains 324152 sequences. (Running on oeis4.)