A165323 a(0)=1, a(1)=8, a(n)=17*a(n-1)-64*a(n-2) for n>1.

1, 8, 72, 712, 7496, 81864, 911944, 10263752, 116119368, 1317149128, 14959895624, 170020681416, 1932918264136, 21978286879688, 249924108049992, 2842099476549832, 32320548186147656, 367554952665320904

Offset: 0

Author

Philippe Deléham, Sep 14 2009

Keywords

• nonn
• easy
• changed

Comments

a(n)/a(n-1) tends to (17+sqrt(33))/2 = 11.3722813...

For n>=2, a(n) equals 8^n times the permanent of the (2n-2) X (2n-2) tridiagonal matrix with 1/sqrt(8)'s along the main diagonal, and 1's along the superdiagonal and the subdiagonal. - John M. Campbell, Jul 08 2011

Links

• Index entries for linear recurrences with constant coefficients, signature (17,-64).

Crossrefs

Cf. A165253.

Programs

Mathematica

LinearRecurrence[{17,-64},{1,8},20] (* Harvey P. Dale, Jun 08 2018 *)

Formula

G.f.: (1-9*x)/(1-17*x+64*x^2).

a(n) = Sum_{k=0..n} A165253(n,k)*8^(n-k).

a(n) = ((33-sqrt(33))*(17+sqrt(33))^n+(33+sqrt(33))*(17-sqrt(33))^n)/(66*2^n). - Klaus Brockhaus, Sep 28 2009