A167120 a(n) = 20*a(n-1) - 64*a(n-2) + 1 for n > 2; a(0) = 1, a(1) = 22, a(2) = 376.

1, 22, 376, 6113, 98197, 1572709, 25169573, 402738085, 6443909029, 103102943141, 1649648684965, 26394385338277, 422310190927781, 6756963156905893, 108111410918739877, 1729782576332820389, 27676521227857055653

Offset

0,2

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).

Formula

a(n) = (4321*16^n - 1460*4^n + 64)/2880, for n > 0.

G.f.: (1 + x - 2*x^2 + x^3)/((1-x)*(1-4*x)*(1-16*x)).

E.g.f.: (1/2880)*(-45 + 64*exp(x) - 1460*exp(4*x) + 4321*exp(16*x)). - G. C. Greubel, Jun 04 2016

a(n) = 21*a(n-1) - 84*a(n-2) + 64*a(n-3). - Wesley Ivan Hurt, Aug 04 2025

Mathematica

CoefficientList[Series[(1 + x - 2*x^2 + x^3)/((1 - x)*(1 - 4*x)*(1 - 16*x)), {x, 0, 10}], x] (* G. C. Greubel, Jun 04 2016 *)
LinearRecurrence[{21, -84, 64}, {1, 22, 376, 6113}, 20] (* Harvey P. Dale, Jul 13 2018 *)

Prog

(Magma) [ n le 2 select 21*n-20 else n eq 3 select 376 else 20*Self(n-1)-64*Self(n-2)+1: n in [1..17] ];
(PARI) a(n)=if(n, ([0, 1, 0; 0, 0, 1; 64, -84, 21]^(n-1)*[22; 376; 6113])[1, 1], 1) \\ Charles R Greathouse IV, May 20 2026

Crossrefs

Cf. A166912, A166913, A167121, A167122.

Sequence in context: A081127 A016196 A238318 * A167121 A167122 A132167

Adjacent sequences: A167117 A167118 A167119 * A167121 A167122 A167123

Keyword

nonn,easy

Author

Klaus Brockhaus, Oct 27 2009

Status

approved