A165311 a(0)=1, a(1)=4, a(n)=9*a(n-1)-16*a(n-2) for n>1.

1, 4, 20, 116, 724, 4660, 30356, 198644, 1302100, 8540596, 56031764, 367636340, 2412218836, 15827788084, 103854591380, 681446713076, 4471346955604, 29338975191220, 192509225431316, 1263159425822324, 8288287225499860

Offset: 0

Author

Philippe Deléham, Sep 14 2009

Keywords

• nonn

Comments

a(n)/a(n-1) tends to (9+sqrt(17))/2 = 6.56155281...

Links

• Index entries for linear recurrences with constant coefficients, signature (9,-16).

Programs

Mathematica

LinearRecurrence[{9,-16},{1,4},30] (* Harvey P. Dale, Feb 19 2015 *)

Formula

G.f.: (1-5x)/(1-9x+16x^2). a(n)=Sum_{k, 0<=k<=n}A165253(n,k)*4^(n-k).

a(n) = ((17-sqrt(17))*(9+sqrt(17))^n+(17+sqrt(17))*(9-sqrt(17))^n )/(34*2^n). [From Klaus Brockhaus, Sep 26 2009]