A337512 G.f. A(x) satisfies: A(x) = 1 - Sum_{k=1..3} (x * A(x))^k.

1, -1, 0, 1, 1, -6, 4, 13, -13, -61, 124, 120, -516, -352, 2848, -923, -11337, 10165, 49352, -88655, -159903, 512430, 450812, -2873276, -11660, 13752804, -9160464, -62238760, 91526344, 239932224, -620180224, -768156379, 3683079807, 1168683353

Offset

0,6

Links

Table of n, a(n) for n=0..33.

Formula

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

Mathematica

nmax = 33; A[_] = 0; Do[A[x_] = 1 - Sum[(x A[x])^k, {k, 1, 3}] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
nmax = 34; CoefficientList[(1/x) InverseSeries[Series[x/(1 - x - x^2 - x^3), {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, 3]; Table[a[n], {n, 0, 33}]

Crossrefs

Cf. A000073, A007440, A036765, A337513, A337514.

Sequence in context: A263586 A180497 A213038 * A131828 A096038 A064462

Adjacent sequences: A337509 A337510 A337511 * A337513 A337514 A337515

Keyword

sign

Author

Ilya Gutkovskiy, Aug 30 2020

Status

approved