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A270473
Expansion of g.f. (1-5*x)/(1-9*x).
4
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
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).
Sequence in context: A093186 A000765 A226283 * A374388 A288269 A189334
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Mar 17 2016
STATUS
approved