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 A286098 Square array read by antidiagonals: A(n,k) = T(n AND k, n OR 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, 1, 1, 3, 4, 3, 6, 6, 6, 6, 10, 11, 12, 11, 10, 15, 15, 17, 17, 15, 15, 21, 22, 21, 24, 21, 22, 21, 28, 28, 28, 28, 28, 28, 28, 28, 36, 37, 38, 37, 40, 37, 38, 37, 36, 45, 45, 47, 47, 49, 49, 47, 47, 45, 45, 55, 56, 55, 58, 59, 60, 59, 58, 55, 56, 55, 66, 66, 66, 66, 70, 70, 70, 70, 66, 66, 66, 66, 78, 79, 80, 79, 78, 83, 84, 83, 78, 79, 80, 79, 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 MathWorld, Pairing Function FORMULA A(n,k) = T(A004198(n,k), A003986(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,  4,   6,  11,  15,  22,  28,  37,  45,  56,  66,  79,  91    3,  6,  12,  17,  21,  28,  38,  47,  55,  66,  80,  93, 105    6, 11,  17,  24,  28,  37,  47,  58,  66,  79,  93, 108, 120   10, 15,  21,  28,  40,  49,  59,  70,  78,  91, 105, 120, 140   15, 22,  28,  37,  49,  60,  70,  83,  91, 106, 120, 137, 157   21, 28,  38,  47,  59,  70,  84,  97, 105, 120, 138, 155, 175   28, 37,  47,  58,  70,  83,  97, 112, 120, 137, 155, 174, 194   36, 45,  55,  66,  78,  91, 105, 120, 144, 161, 179, 198, 218   45, 56,  66,  79,  91, 106, 120, 137, 161, 180, 198, 219, 239   55, 66,  80,  93, 105, 120, 138, 155, 179, 198, 220, 241, 261   66, 79,  93, 108, 120, 137, 155, 174, 198, 219, 241, 264, 284   78, 91, 105, 120, 140, 157, 175, 194, 218, 239, 261, 284, 312 MATHEMATICA T[a_, b_]:=((a + b)^2 + 3a + b)/2; A[n_, k_]:=T[BitAnd[n, k], BitOr[n,  k]]; Table[A[n - k, k], {n, 0, 20}, {k, 0, n}] // Flatten (* Indranil Ghosh, May 21 2017 *) PROG (Scheme) (define (A286098 n) (A286098bi (A002262 n) (A025581 n))) (define (A286098bi row col) (let ((a (A004198bi row col)) (b (A003986bi 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. A000217 (row 0 & column 0), A084263 (seems to be row 1 & column 1), A046092 (main diagonal). Cf. A003056, A003986, A004198. Cf. also arrays A286099, A286101, A286102, A286108. Sequence in context: A005092 A136195 A117892 * A074372 A049276 A101684 Adjacent sequences:  A286095 A286096 A286097 * A286099 A286100 A286101 KEYWORD nonn,tabl AUTHOR Antti Karttunen, May 03 2017 STATUS approved

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Last modified June 20 17:27 EDT 2019. Contains 324234 sequences. (Running on oeis4.)