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A218722

a(n) = (19^n-1)/18.

0, 1, 20, 381, 7240, 137561, 2613660, 49659541, 943531280, 17927094321, 340614792100, 6471681049901, 122961939948120, 2336276859014281, 44389260321271340, 843395946104155461, 16024522975978953760, 304465936543600121441

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OFFSET

0,3

COMMENTS

Partial sums of powers of 19 (A001029); q-integers for q=19: diagonal k=1 in triangle A022183.

Partial sums are in A014903. Also, the sequence is related to A014936 by A014936(n) = n*a(n)-sum(a(i), i=0..n-1) for n>0. - Bruno Berselli, Nov 06 2012

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..700

Index entries related to partial sums

Index entries for linear recurrences with constant coefficients, signature (20,-19).

FORMULA

a(n) = floor(19^n/18).

G.f.: x/((1-x)*(1-19*x)). - Bruno Berselli, Nov 06 2012

a(n) = 20*a(n-1) - 19*a(n-2). - Vincenzo Librandi, Nov 07 2012

E.g.f.: exp(10*x)*sinh(9*x)/9. - Stefano Spezia, Mar 11 2023

MATHEMATICA

LinearRecurrence[{20, -19}, {0, 1}, 40] (* Vincenzo Librandi, Nov 07 2012 *)

PROG