A165312 a(0)=1, a(1)=5, a(n)=11*a(n-1)-25*a(n-2) for n>1.

1, 5, 30, 205, 1505, 11430, 88105, 683405, 5314830, 41378005, 322287305, 2510710230, 19560629905, 152399173205, 1187375157630, 9251147403805, 72078242501105, 561581982417030, 4375445744059705, 34090353624231005

Offset: 0

Author

Philippe Deléham, Sep 14 2009

Keywords

• nonn

Comments

a(n)/a(n-1) tends to (11+sqrt(21))/2 = 7.79128784...

For n>=2, a(n) equals 5^n times the permanent of the (2n-2)X(2n-2) tridiagonal matrix with 1/sqrt(5)'s along the main diagonal, and 1's along the superdiagonal and the subdiagonal. [John M. Campbell, Jul 08 2011]

Links

• Indranil Ghosh, Table of n, a(n) for n = 0..1119
• Index entries for linear recurrences with constant coefficients, signature (11,-25).

Crossrefs

Cf. A165253.

Programs

Mathematica

LinearRecurrence[{11,-25},{1,5},30] (* Harvey P. Dale, Oct 02 2016 *)

Formula

G.f.: (1-6x)/(1-11x+25x^2).

a(n) = Sum_{k=0..n} A165253(n,k)*5^(n-k).

a(n) = ((21-sqrt(21))*(11+sqrt(21))^n+(21+sqrt(21))*(11-sqrt(21))^n )/(42*2^n). [Klaus Brockhaus, Sep 26 2009]