A270576 Expansion of g.f. (1+2*x)/(1-6*x).

1, 8, 48, 288, 1728, 10368, 62208, 373248, 2239488, 13436928, 80621568, 483729408, 2902376448, 17414258688, 104485552128, 626913312768, 3761479876608, 22568879259648, 135413275557888, 812479653347328, 4874877920083968, 29249267520503808, 175495605123022848, 1052973630738137088

Offset: 0

Author

Colin Barker, Mar 19 2016

Keywords

• nonn
• easy

Comments

Partial sums are 1, 9, 57, 345, 2073, 12441, ...

Essentially the same as A084477. - R. J. Mathar, Mar 21 2016

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6).

Crossrefs

Cf. A000400 (powers of 6), A003949: (1+x)/(1-6*x), A084477.

Programs

PARI

Vec((1+2*x)/(1-6*x) + O(x^30))

Formula

G.f.: (1+2*x)/(1-6*x).

a(n) = 6*a(n-1) for n>1.

a(n) = 8*6^(n-1) for n>0.

E.g.f.: (4*exp(6*x) - 1)/3. - Elmo R. Oliveira, Mar 25 2025