A166965 a(n) = 20*a(n-1) - 64*a(n-2) for n > 1; a(0) = 1, a(1) = 19.

1, 19, 316, 5104, 81856, 1310464, 20970496, 335540224, 5368692736, 85899280384, 1374389272576, 21990231506944, 351843716694016, 5629499517435904, 90071992480301056, 1441151880490123264, 23058430091063197696

Offset: 0

Author

Klaus Brockhaus, Oct 25 2009

Keywords

• nonn

Comments

lim_{n -> infinity} a(n)/a(n-1) = 16.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (20, -64).

Crossrefs

Cf. A166927, A006105 (Gaussian binomial coefficient [ n, 2 ] for q=4).

Programs

Magma

[ n le 2 select 18*n-17 else 20*Self(n-1)-64*Self(n-2): n in [1..17] ];

Mathematica

LinearRecurrence[{20,-64},{1,19},20] (* Harvey P. Dale, Aug 24 2014 *)

Formula

a(n) = (5*16^n - 4^n)/4.

G.f.: (1-x)/((1-4*x)*(1-16*x)).

E.g.f.: (1/4)*(5*exp(16*x) - exp(4*x)). - G. C. Greubel, May 29 2016