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A352043
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a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/4)} binomial(n-3*k-1,k) * a(k).
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1
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1, 1, 1, 1, 1, 2, 3, 4, 5, 7, 10, 14, 19, 26, 36, 50, 69, 95, 131, 181, 250, 346, 482, 678, 963, 1380, 1994, 2903, 4252, 6254, 9222, 13616, 20109, 29681, 43755, 64394, 94583, 138632, 202755, 295906, 430986, 626585, 909500, 1318384, 1909042, 2762122, 3994290
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OFFSET
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0,6
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LINKS
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FORMULA
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G.f. A(x) satisfies: A(x) = 1 + x * A(x^4/(1 - x)) / (1 - x).
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MATHEMATICA
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a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 3 k - 1, k] a[k], {k, 0, Floor[(n - 1)/4]}]; Table[a[n], {n, 0, 46}]
nmax = 46; A[_] = 0; Do[A[x_] = 1 + x A[x^4/(1 - x)]/(1 - x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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