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A307044
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a(n) = Sum_{k=0..floor(n/8)} (-1)^k*binomial(n,8*k).
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2
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1, 1, 1, 1, 1, 1, 1, 1, 0, -8, -44, -164, -494, -1286, -3002, -6434, -12868, -24292, -43604, -74612, -121124, -183140, -245156, -245156, 0, 961376, 3749136, 10814896, 27293176, 63453016, 138975976, 290021896, 580043792, 1114351888, 2054677648, 3619173776
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OFFSET
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0,10
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LINKS
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FORMULA
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G.f.: (1 - x)^7/((1 - x)^8 + x^8).
a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - 2*a(n-8) for n > 7.
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MATHEMATICA
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a[n_] := Sum[(-1)^k * Binomial[n, 8*k], {k, 0, Floor[n/8]}]; Array[a, 36, 0] (* Amiram Eldar, May 25 2021 *)
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PROG
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(PARI) {a(n) = sum(k=0, n\8, (-1)^k*binomial(n, 8*k))}
(PARI) N=66; x='x+O('x^N); Vec((1-x)^7/((1-x)^8+x^8))
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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