A270473 Expansion of g.f. (1-5*x)/(1-9*x).

1, 4, 36, 324, 2916, 26244, 236196, 2125764, 19131876, 172186884, 1549681956, 13947137604, 125524238436, 1129718145924, 10167463313316, 91507169819844, 823564528378596, 7412080755407364, 66708726798666276, 600378541187996484, 5403406870691968356, 48630661836227715204

Offset: 0

Author

Colin Barker, Mar 17 2016

Keywords

• nonn
• easy

Comments

Also squares that can be expressed as the sum of two powers of three (3^x + 3^y), except a(0). - Karl-Heinz Hofmann, Sep 03 2022

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (9).

Crossrefs

Cf. A001019 (powers of 9), A083884 (partial sums).

Cf. A067403: (1-4*x)/(1-9*x); A102518: (1-6*x)/(1-9*x).

Cf. A356879, A356880.

Programs

Mathematica

Join[{1},NestList[9#&,4,20]] (* Harvey P. Dale, Oct 23 2022 *)

PARI

Vec((1-5*x)/(1-9*x) + O(x^30))

Formula

G.f.: (1-5*x)/(1-9*x).

a(n) = 9*a(n-1) for n>1.

a(n) = 4*9^(n-1) for n>0.

E.g.f.: (4*exp(9*x) + 5)/9. - Stefano Spezia, Jul 09 2024