A167033 a(n) = 20*a(n-1) - 64*a(n-2) + 3 for n > 1; a(0) = 1, a(1) = 22.

1, 22, 379, 6175, 99247, 1589743, 25443055, 407117551, 6513995503, 104224386799, 1667592023791, 26681479720687, 426903704891119, 6830459395698415, 109287350800936687, 1748597614694035183, 27977561842620755695

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, A167031, A167032.

Programs

Magma

[ n le 2 select 21*n-20 else 20*Self(n-1)-64*Self(n-2)+3: n in [1..17] ];

Mathematica

LinearRecurrence[{21, -84, 64}, {1, 22, 379}, 50] (* G. C. Greubel, May 30 2016 *)

Formula

a(n) = (91*16^n - 35*4^n + 4)/60.

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-3).

E.g.f.: (1/60)*(91*exp(16*x) - 35*exp(4*x) + 4*exp(x)). (End)