A337513 G.f. A(x) satisfies: A(x) = 1 - Sum_{k=1..4} (x * A(x))^k.

1, -1, 0, 1, 0, -1, -5, 13, 5, -43, 4, 98, 122, -638, -246, 2912, -537, -9419, -1648, 47005, 2243, -232237, 87988, 904267, -351692, -4123026, 1726126, 20257940, -14035151, -86846040, 73352891, 387126945, -358259621, -1853868355, 2081413376

Offset: 0

Author

Ilya Gutkovskiy, Aug 30 2020

Keywords

• sign

Crossrefs

Cf. A000078, A007440, A036766, A337512, A337514.

Programs

Mathematica

nmax = 34; A[] = 0; Do[A[x] = 1 - Sum[(x A[x])^k, {k, 1, 4}] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
nmax = 35; CoefficientList[(1/x) InverseSeries[Series[x/(1 - x - x^2 - x^3 - x^4), {x, 0, nmax}], x], x]
b[m_, r_, k_] := b[m, r, k] = If[m + r == 0, 1, Sum[b[m - j, r + j - 1, k], {j, 1, Min[1, m]}] - Sum[b[m + j - 1, r - j, k], {j, 1, Min[k, r]}]]; a[n_] := b[0, n, 4]; Table[a[n], {n, 0, 34}]

Formula

G.f.: A(x) = (1/x) * Series_Reversion(x / (1 - x - x^2 - x^3 - x^4)).