A351345 G.f. A(x) satisfies: A(x) = 1 + x + x^2 + x^3 + x^4 + x^5 + x^6 * A(x/(1 - 2*x)) / (1 - 2*x).

1, 1, 1, 1, 1, 1, 1, 3, 9, 27, 81, 243, 729, 2189, 6601, 20141, 63009, 205989, 718905, 2720543, 11183601, 49321367, 228895201, 1097860903, 5371546897, 26598018425, 132755261681, 667027581401, 3376011676481, 17249045903945, 89270689572497, 470069622480667

Offset

0,8

Comments

Shifts 6 places left under 2nd-order binomial transform.

Links

Table of n, a(n) for n=0..31.

Formula

a(0) = ... = a(5) = 1; a(n) = Sum_{k=0..n-6} binomial(n-6,k) * 2^k * a(n-k-6).

Mathematica

nmax = 31; A[_] = 0; Do[A[x_] = 1 + x + x^2 + x^3 + x^4 + x^5 + x^6 A[x/(1 - 2 x)]/(1 - 2 x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[n_] := a[n] = If[n < 6, 1, Sum[Binomial[n - 6, k] 2^k a[n - k - 6], {k, 0, n - 6}]]; Table[a[n], {n, 0, 31}]

Crossrefs

Cf. A004211, A007472, A010750, A210543, A275936, A351342, A351343, A351344

Sequence in context: A352779 A050733 A238939 * A351344 A079846 A067500

Adjacent sequences: A351342 A351343 A351344 * A351346 A351347 A351348

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 08 2022

Status

approved