A351343 G.f. A(x) satisfies: A(x) = 1 + x + x^2 + x^3 + x^4 * A(x/(1 - 2*x)) / (1 - 2*x).

1, 1, 1, 1, 1, 3, 9, 27, 81, 245, 761, 2493, 8849, 34519, 147057, 670327, 3198561, 15732905, 79174929, 407127897, 2145061729, 11635963499, 65309080185, 380583443187, 2304629301041, 14475031232285, 93943897651017, 627220447621973, 4290783719133041, 29988917377046207

Offset

0,6

Comments

Shifts 4 places left under 2nd-order binomial transform.

Links

Table of n, a(n) for n=0..29.

Formula

a(0) = ... = a(3) = 1; a(n) = Sum_{k=0..n-4} binomial(n-4,k) * 2^k * a(n-k-4).

Mathematica

nmax = 29; A[_] = 0; Do[A[x_] = 1 + x + x^2 + x^3 + x^4 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 < 4, 1, Sum[Binomial[n - 4, k] 2^k a[n - k - 4], {k, 0, n - 4}]]; Table[a[n], {n, 0, 29}]

Crossrefs

Cf. A004211, A007472, A010748, A210541, A275934, A351342, A351344, A351345.

Sequence in context: A079846 A067500 A273898 * A078226 A083591 A052917

Adjacent sequences: A351340 A351341 A351342 * A351344 A351345 A351346

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 08 2022

Status

approved