A270568 Expansion of g.f. (1+4*x)/(1-8*x).

1, 12, 96, 768, 6144, 49152, 393216, 3145728, 25165824, 201326592, 1610612736, 12884901888, 103079215104, 824633720832, 6597069766656, 52776558133248, 422212465065984, 3377699720527872, 27021597764222976, 216172782113783808, 1729382256910270464, 13835058055282163712

Offset: 0

Author

Colin Barker, Mar 19 2016

Keywords

• nonn
• easy

Comments

Partial sums are 1, 13, 109, 877, 7021, 56173, ...

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (8).

Crossrefs

Cf. A001018 (powers of 8), A094085, A204623.

Programs

Mathematica

CoefficientList[Series[(1 + 4 x)/(1 - 8 x), {x, 0, 20}], x] (* Michael De Vlieger, Mar 19 2016 *)
Join[{1},NestList[8#&,12,30]] (* Harvey P. Dale, Oct 05 2022 *)

PARI

Vec((1+4*x)/(1-8*x) + O(x^30))

Formula

G.f.: (1+4*x)/(1-8*x).

a(n) = 8*a(n-1) for n>1.

a(n) = 12*8^(n-1) for n>0.

a(n) = A094085(n), n>1. - R. J. Mathar, Mar 21 2016

E.g.f.: (3*exp(8*x) - 1)/2. - Elmo R. Oliveira, Mar 25 2025