A351049 G.f. A(x) satisfies: A(x) = 1 + x + x^2 * A(x/(1 - 3*x)) / (1 - 3*x).

1, 1, 1, 4, 16, 67, 307, 1585, 9235, 59548, 415564, 3094807, 24452785, 204611653, 1810429597, 16892405896, 165592138372, 1698918207403, 18184602679435, 202577753111653, 2344503929765023, 28146188358379120, 349996346545057288, 4501360727764475503

Offset

0,4

Comments

Shifts 2 places left under 3rd-order binomial transform.

Links

Seiichi Manyama, Table of n, a(n) for n = 0..540

Formula

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

Mathematica

nmax = 23; A[_] = 0; Do[A[x_] = 1 + x + x^2 A[x/(1 - 3 x)]/(1 - 3 x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = a[1] = 1; a[n_] := a[n] = Sum[Binomial[n - 2, k] 3^k a[n - k - 2], {k, 0, n - 2}]; Table[a[n], {n, 0, 23}]

Crossrefs

Cf. A004212, A007472, A007476, A351050.

Sequence in context: A091153 A270765 A292759 * A259815 A283036 A307051

Adjacent sequences: A351046 A351047 A351048 * A351050 A351051 A351052

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 30 2022

Status

approved