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

0,2

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).

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

Mathematica

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

Prog

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

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.

Sequence in context: A093186 A000765 A226283 * A374388 A288269 A189334

Adjacent sequences: A270470 A270471 A270472 * A270474 A270475 A270476

Keyword

nonn,easy

Author

Colin Barker, Mar 17 2016

Status

approved