A163192 a(n) = 20*a(n-1)-93*a(n-2) for n > 1; a(0) = 1, a(1) = 10.

1, 10, 107, 1210, 14249, 172450, 2123843, 26439010, 331262801, 4166428090, 52521121307, 662944613770, 8374427993849, 105834710796370, 1337872412499443, 16914820145926450, 213874268556080801

Offset

0,2

Comments

Binomial transform of A152266. Tenth binomial transform of powers of 7 interleaved with zeros.

Links

Harvey P. Dale, Table of n, a(n) for n = 0..900

Index entries for linear recurrences with constant coefficients, signature (20, -93).

Formula

a(n) = ((10+sqrt(7))^n+(10-sqrt(7))^n)/2.

G.f.: (1-10*x)/(1-20*x+93*x^2).

Mathematica

LinearRecurrence[{20, -93}, {1, 10}, 40] (* Harvey P. Dale, Nov 01 2011 *)

Prog

(Magma) [ n le 2 select 9*n-8 else 20*Self(n-1)-93*Self(n-2): n in [1..17] ];
(PARI) a(n)=([0, 1; -93, 20]^n*[1; 10])[1, 1] \\ Charles R Greathouse IV, Jun 05 2026

Crossrefs

Cf. A152266, A000420 (powers of 7).

Sequence in context: A078192 A238107 A015589 * A140647 A177060 A322641

Adjacent sequences: A163189 A163190 A163191 * A163193 A163194 A163195

Keyword

nonn,easy,changed

Author

Klaus Brockhaus, Jul 22 2009

Status

approved