A349036 - OEIS

A349036

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

1, 1, 2, 0, 17, 29, 1459, -4233, 1056763, 11355763, 6957281732, -209598234798, 410408244241271, 37950250148465939, 218184080600974976674, -60068553848055713514168, 1043447774597599997266176403, 864004926526955255880635472763, 44918734284964096829849186288888390

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..18.

FORMULA

a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-2} (-3)^k * a(k) * a(n-k-2).

MATHEMATICA

nmax = 18; A[_] = 0; Do[A[x_] = 1/(1 - x - x^2 A[-3 x]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

a[0] = 1; a[n_] := a[n] = a[n - 1] + Sum[(-3)^k a[k] a[n - k - 2], {k, 0, n - 2}]; Table[a[n], {n, 0, 18}]

CROSSREFS

Cf. A001006, A015098, A348879, A349035, A349037.