A348861 G.f. A(x) satisfies: A(x) = 1 / ((1 + x) * (1 - x * A(3*x))).

1, 0, 1, 9, 253, 20754, 5064301, 3696964686, 8088964208893, 53079786931826952, 1044822534120774924517, 61696770693051062357722413, 10929459535778338593167921597497, 5808373834674826377471903826388912406, 9260429805605038398327449254849233420999649

Offset: 0

Author

Ilya Gutkovskiy, Nov 02 2021

Keywords

• nonn

Crossrefs

Cf. A005043, A015084, A348860, A348862.

Programs

Mathematica

nmax = 14; A[] = 0; Do[A[x] = 1/((1 + x) (1 - x A[3 x])) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[n_] := a[n] = (-1)^n + Sum[3^k a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 14}]

Formula

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

a(n) ~ c * 3^(n*(n-1)/2), where c = 0.353669086629957226916356822657293915192042094460583129054709983118948... - Vaclav Kotesovec, Nov 02 2021