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A286098
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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).
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5
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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
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OFFSET
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0,4
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COMMENTS
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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), ...
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LINKS
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FORMULA
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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, ...].
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EXAMPLE
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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
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MATHEMATICA
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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 *)
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PROG
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(Scheme)
(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 range(0, 21): print [A(k, n - k) for k in range(0, n + 1)] # Indranil Ghosh, May 21 2017
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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