A167122 a(n) = 20*a(n-1) - 64*a(n-2) + 3 for n > 2; a(0) = 1, a(1) = 22, a(2) = 378.

1, 22, 378, 6155, 98911, 1584303, 25355759, 405719791, 6491627247, 103866478319, 1661865422575, 26589853839087, 425437689736943, 6807003149037295, 108912050837581551, 1742592815213244143, 27881485050659663599

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) = (1451*16^n - 540*4^n + 64)/960, for n > 0.

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

E.g.f.: (1/960)*(-15 + 64*exp(x) - 540*exp(4*x) + 1451*exp(16*x)). - G. C. Greubel, Jun 04 2016

Mathematica

CoefficientList[Series[(1 + x + 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, 378, 6155}, 20] (* Harvey P. Dale, Sep 26 2023 *)

Prog

(Magma) [ n le 2 select 21*n-20 else n eq 3 select 378 else 20*Self(n-1)-64*Self(n-2)+3: n in [1..17] ];
(PARI) a(n)=if(n, ([0, 1, 0; 0, 0, 1; 64, -84, 21]^(n-1)*[22; 378; 6155])[1, 1], 1) \\ Charles R Greathouse IV, May 20 2026

Crossrefs

Cf. A166912, A166913, A167120, A167121.

Sequence in context: A238318 A167120 A167121 * A132167 A167033 A222886

Adjacent sequences: A167119 A167120 A167121 * A167123 A167124 A167125

Keyword

nonn,easy

Author

Klaus Brockhaus, Oct 27 2009

Status

approved