A167031 a(n) = 20*a(n-1) - 64*a(n-2) + 1 for n > 1; a(0) = 1, a(1) = 20.

1, 20, 337, 5461, 87653, 1403557, 22461349, 359399333, 5750460325, 92007649189, 1472123522981, 23553980911525, 376863712759717, 6029819476856741, 96477111920512933, 1543633791891427237, 24698140674915717029

Offset: 0

Author

Klaus Brockhaus, Oct 27 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 (21,-84,64).

Crossrefs

Cf. A166915, A166916, A006105, A167032, A167033.

Programs

Magma

[ n le 2 select 19*n-18 else 20*Self(n-1)-64*Self(n-2)+1: n in [1..17] ];

Mathematica

LinearRecurrence[{21, -84, 64}, {1, 20, 337}, 50] (* G. C. Greubel, May 30 2016 *)

Formula

a(n) = (241*16^n - 65*4^n + 4)/180.

G.f.: (1-x+x^2)/((1-x)*(1-4*x)*(1-16*x)).

From G. C. Greubel, May 30 2016: (Start)

a(n) = 21*a(n-1) - 84*a(n-2) + 64*a(n-2).

E.g.f.: (1/180)*(241*exp(16*x) - 65*exp(4*x) + 4*exp(x)). (End)