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

Offset: 0

Author

M. F. Hasler, Nov 04 2012

Keywords

• nonn
• easy

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).

Crossrefs

Cf. similar sequences of the form (k^n-1)/(k-1): A000225, A003462, A002450, A003463, A003464, A023000, A023001, A002452, A002275, A016123, A016125, A091030, A135519, A135518, A131865, A091045, A218721, A064108, A218724-A218734, A132469, A218736-A218753, A133853, A094028, A218723.

Cf. A001029, A014903, A014936, A022183.

Programs

Magma

[n le 2 select n-1 else 20*Self(n-1)-19*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Nov 07 2012

Mathematica

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

Maxima

A218722(n):=(19^n-1)/18$ makelist(A218722(n),n,0,30); /* Martin Ettl, Nov 05 2012 */

PARI

A218722(n)=19^n\18

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