A167121 a(n) = 20*a(n-1) - 64*a(n-2) + 2 for n > 2; a(0) = 1, a(1) = 22, a(2) = 377.

1, 22, 377, 6134, 98554, 1578506, 25262666, 404228938, 6467768138, 103484710730, 1655757053770, 26492119588682, 423873940332362, 6781983152971594, 108511730878160714, 1736187695773032266, 27779003139258359626

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) = (4337*16^n - 1540*4^n + 128)/2880, for n > 0.

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

E.g.f.: (1/2880)*(-45 + 128*exp(x) - 1540*exp(4*x) + 4337*exp(16*x)). - G. C. Greubel, Jun 04 2016

Mathematica

CoefficientList[Series[(1 + x - x^2 + x^3)/((1-x)*(1-4*x)*(1-16*x)), {x, 0, 10}], x] (* G. C. Greubel, Jun 04 2016 *)
Join[{1}, RecurrenceTable[{a[1]==22, a[2]==377, a[n]==20a[n-1]-64a[n-2]+2}, a, {n, 20}]] (* Harvey P. Dale, Apr 01 2019 *)

Prog

(Magma) [ n le 2 select 21*n-20 else n eq 3 select 377 else 20*Self(n-1)-64*Self(n-2)+2: n in [1..17] ];
(PARI) a(n)=if(n, ([0, 1, 0; 0, 0, 1; 64, -84, 21]^(n-1)*[22; 377; 6134])[1, 1], 1) \\ Charles R Greathouse IV, May 20 2026

Crossrefs

Cf. A166912, A166913, A167120, A167122.

Sequence in context: A016196 A238318 A167120 * A167122 A132167 A167033

Adjacent sequences: A167118 A167119 A167120 * A167122 A167123 A167124

Keyword

nonn,easy

Author

Klaus Brockhaus, Oct 27 2009

Status

approved