A178510 a(n+1) = a(n)*100 + 21^n, with a(1)=1.

1, 121, 12541, 1263361, 126530581, 12657142201, 1265799986221, 126581799710641, 12658217793923461, 1265822573672392681, 126582274047120246301, 12658227754989525172321, 1265822782854780028618741, 126582278439950380600993561, 12658227847238957992620864781

Offset: 1

Author

Mark Dols, May 29 2010

Keywords

• nonn
• easy

Comments

Related to decimal expansion of fraction 1/79 and Pell numbers.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200
• Index entries for linear recurrences with constant coefficients, signature (121,-2100).

Crossrefs

Cf. A000129, A021083, A038207.

Programs

Magma

[(1/79)*(100^n-21^n): n in [1..20]]; // Vincenzo Librandi, Sep 13 2011

Mathematica

Rest[RecurrenceTable[{a[0]==0,a[n]==100a[n-1]+21^(n-1)},a[n],{n,15}]] (* or *) LinearRecurrence[{121,-2100},{1,121},20] (* Harvey P. Dale, Sep 09 2011 *)

PARI

a(n)=(100^n-21^n)/79 \\ Charles R Greathouse IV, Oct 10 2011

Formula

a(n) = 121*a(n-1) - 2100*a(n-2). - Harvey P. Dale, Sep 09 2011

G.f.: x/(1 - 121*x + 2100*x^2). - Philippe Deléham, Oct 11 2011

Extensions

Removed vacuous a(0)=0 from NAME. - R. J. Mathar, Jun 19 2021