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A229654
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Quadrisection a(4n+k) gives k-th differences of a for k=0..3 with a(n)=0 for n<3 and a(3)=1.
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8
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0, 0, 0, 1, 0, 0, 1, -3, 0, 1, -2, 3, 1, -1, 1, 0, 0, 0, 1, -6, 0, 1, -5, 12, 1, -4, 7, -9, -3, 3, -2, -2, 0, 1, -4, 12, 1, -3, 8, -15, -2, 5, -7, 7, 3, -2, 0, 4, 1, -2, 4, -7, -1, 2, -3, 4, 1, -1, 1, -1, 0, 0, 0, 1, 0, 0, 1, -9, 0, 1, -8, 21, 1, -7, 13, -18
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OFFSET
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0,8
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LINKS
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FORMULA
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a(4*n) = a(n),
a(4*n+1) = a(n+1) - a(n),
a(4*n+2) = a(n+2) - 2*a(n+1) + a(n),
a(4*n+3) = a(n+3) - 3*a(n+2) + 3*a(n+1) - a(n).
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MAPLE
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a:= proc(n) option remember; (m-> `if`(n<4, `if`(n=3, 1, 0), add(
a(q+m-j)*(-1)^j*binomial(m, j), j=0..m)))(irem(n, 4, 'q'))
end:
seq(a(n), n=0..100);
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MATHEMATICA
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a[n_] := a[n] = Module[{ m, q}, {q, m} = QuotientRemainder[n, 4]; If[n < 4, If[n == 3, 1, 0], Sum[a[q + m - j]*(-1)^j*Binomial[m, j], {j, 0, m}]]];
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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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