A351344 G.f. A(x) satisfies: A(x) = 1 + x + x^2 + x^3 + x^4 + x^5 * A(x/(1 - 2*x)) / (1 - 2*x).

1, 1, 1, 1, 1, 1, 3, 9, 27, 81, 243, 731, 2223, 6939, 22727, 79971, 306929, 1282815, 5744361, 26984415, 130656409, 644739377, 3224303841, 16318576681, 83717193681, 436948772697, 2331807007139, 12791837178265, 72472130039123, 425239734375217, 2584950704996379

Offset

0,7

Comments

Shifts 5 places left under 2nd-order binomial transform.

Links

Table of n, a(n) for n=0..30.

Formula

a(0) = ... = a(4) = 1; a(n) = Sum_{k=0..n-5} binomial(n-5,k) * 2^k * a(n-k-5).

Mathematica

nmax = 30; A[_] = 0; Do[A[x_] = 1 + x + x^2 + x^3 + x^4 + x^5 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 < 5, 1, Sum[Binomial[n - 5, k] 2^k a[n - k - 5], {k, 0, n - 5}]]; Table[a[n], {n, 0, 30}]

Crossrefs

Cf. A004211, A007472, A010749, A210542, A275935, A351342, A351343, A351345.

Sequence in context: A050733 A238939 A351345 * A079846 A067500 A273898

Adjacent sequences: A351341 A351342 A351343 * A351345 A351346 A351347

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 08 2022

Status

approved