A351755 G.f. A(x) satisfies: A(x) = 1 + x + x^2 + x^3 + x^4 + x^5 + x^6 * A(x/(1 - x)) / (1 - x)^2.

1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31, 63, 127, 257, 535, 1187, 2891, 7751, 22331, 66997, 204473, 626917, 1922395, 5899579, 18192715, 56739881, 180434023, 590010059, 1997588833, 7026454733, 25650892255, 96720885037, 374163527473, 1475021500693, 5893462132221

Offset

0,8

Links

Table of n, a(n) for n=0..34.

Formula

a(0) = ... = a(5) = 1; a(n) = Sum_{k=0..n-6} binomial(n-5,k+1) * a(k).

Mathematica

nmax = 34; A[_] = 0; Do[A[x_] = 1 + x + x^2 + x^3 + x^4 + x^5 + x^6 A[x/(1 - x)]/(1 - x)^2 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[n_] := a[n] = If[n < 6, 1, Sum[Binomial[n - 5, k + 1] a[k], {k, 0, n - 6}]]; Table[a[n], {n, 0, 34}]

Crossrefs

Cf. A040027, A210543, A351437, A351660, A351707, A351754.

Sequence in context: A123121 A117060 A178460 * A057613 A325920 A351754

Adjacent sequences: A351752 A351753 A351754 * A351756 A351757 A351758

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 18 2022

Status

approved