A163414 a(n) = 16*a(n-1) - 62*a(n-2) for n>1, a(0)=1, a(1)=12.

1, 12, 130, 1336, 13316, 130224, 1257992, 12053984, 114868240, 1090544832, 10326886432, 97616403328, 921595494464, 8693310905088, 81954053824640, 772279585078784, 7275322024132864, 68523818111241216, 645311124283621888

Offset: 0

Author

Klaus Brockhaus, Jul 27 2009

Keywords

• nonn
• easy

Comments

Binomial transform of A163413. Inverse binomial transform of A163415.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (16, -62).

Crossrefs

Cf. A163413, A163415.

Programs

Magma

[n le 2 select 11*n-10 else 16*Self(n-1)-62*Self(n-2): n in [1..19]];

Mathematica

LinearRecurrence[{16,-62}, {1,12}, 50] (* G. C. Greubel, Dec 21 2016 *)

PARI

Vec((1-4*x)/(1-16*x+62*x^2) + O(x^50)) \\ G. C. Greubel, Dec 21 2016

Formula

a(n) = ((1+2*sqrt(2))*(8+sqrt(2))^n + (1-2*sqrt(2))*(8-sqrt(2))^n)/2.

G.f.: (1-4*x)/(1-16*x+62*x^2).

E.g.f.: exp(8*x)*( cosh(sqrt(2)*x) + 2*sqrt(2)*sinh(sqrt(2)*x) ). - G. C. Greubel, Dec 21 2016