A344492 a(n) = 1 + Sum_{k=0..n-5} binomial(n-4,k) * a(k).

1, 1, 1, 1, 1, 2, 4, 8, 16, 32, 70, 170, 452, 1277, 3731, 11145, 34031, 106888, 348016, 1180538, 4173726, 15320402, 58053312, 225891952, 899492200, 3660479037, 15228099789, 64831944993, 282763031581, 1263953233142, 5788015999020, 27121892020940, 129849269955372, 634208223729772

Offset

0,6

Links

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

Formula

G.f. A(x) satisfies: A(x) = (1 + x^4 * A(x/(1 - x))) / ((1 - x) * (1 + x^4)).

Mathematica

a[n_] := a[n] = 1 + Sum[Binomial[n - 4, k] a[k] , {k, 0, n - 5}]; Table[a[n], {n, 0, 33}]
nmax = 33; A[_] = 0; Do[A[x_] = (1 + x^4 A[x/(1 - x)])/((1 - x) (1 + x^4)) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

Crossrefs

Cf. A000629, A210542, A344489, A344490, A344491, A344493.

Sequence in context: A100139 A274860 A076766 * A359389 A275072 A290555

Adjacent sequences: A344489 A344490 A344491 * A344493 A344494 A344495

Keyword

nonn

Author

Ilya Gutkovskiy, May 21 2021

Status

approved