A163306 a(n) = 12*a(n-1) - 31*a(n-2) for n > 1; a(0) = 1, a(1) = 7.

1, 7, 53, 419, 3385, 27631, 226637, 1863083, 15331249, 126219415, 1039364261, 8559569267, 70494539113, 580587822079, 4781723152445, 39382455344891, 324356046412897, 2671416441263143, 22001959856357909, 181209608597137475

Offset: 0

Author

Klaus Brockhaus, Jul 24 2009

Keywords

• nonn
• easy

Comments

Binomial transform of A090041. Inverse binomial transform of A163307.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (12,-31).

Crossrefs

Cf. A090041, A163307.

Programs

Magma

[ n le 2 select 6*n-5 else 12*Self(n-1)-31*Self(n-2): n in [1..20] ];

Mathematica

LinearRecurrence[{12,-31}, {1,7}, 50] (* G. C. Greubel, Dec 18 2016 *)

PARI

Vec((1-5*x)/(1-12*x+31*x^2) + O(x^50)) \\ G. C. Greubel, Dec 18 2016

Formula

a(n) = ((5+sqrt(5))*(6+sqrt(5))^n + (5-sqrt(5))*(6-sqrt(5))^n)/10.

G.f.: (1-5*x)/(1-12*x+31*x^2).

E.g.f.: (1/5)*exp(6*x)*(5*cosh(sqrt(5)*x) + sqrt(5)*sinh(sqrt(5)*x)). - G. C. Greubel, Dec 18 2016