A163413 a(n) = 14*a(n-1) - 47*a(n-2) for n > 1; a(0) = 1, a(1) = 11.

1, 11, 107, 981, 8705, 75763, 651547, 5560797, 47228449, 399840827, 3378034475, 28499963781, 240231872609, 2023747918819, 17041572850843, 143465867727309, 1207568224192705, 10163059355514347, 85527124440143723

Offset: 0

Author

Klaus Brockhaus, Jul 27 2009

Keywords

• nonn
• easy

Comments

Binomial transform of A163412. Inverse binomial transform of A163414.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (14, -47).

Crossrefs

Cf. A163412, A163414.

Programs

Magma

[ n le 2 select 10*n-9 else 14*Self(n-1)-47*Self(n-2): n in [1..19] ];

Mathematica

LinearRecurrence[{14,-47}, {1,11}, 50] (* G. C. Greubel, Dec 21 2016 *)

PARI

Vec((1-3*x)/(1-14*x+47*x^2) + O(x^50)) \\ G. C. Greubel, Dec 21 2016

Formula

a(n) = ((1+2*sqrt(2))*(7+sqrt(2))^n + (1-2*sqrt(2))*(7-sqrt(2))^n)/2.

G.f.: (1-3*x)/(1-14*x+47*x^2).

E.g.f.: exp(7*x)*( cosh(sqrt(2)*x) + 2*sqrt(2)*sinh(sqrt(2)*x) ). - G. C. Greubel, Dec 21 2016