A163459 a(n) = 14*a(n-1) - 47*a(n-2) for n > 1; a(0) = 1, a(1) = 8.

1, 8, 65, 534, 4421, 36796, 307357, 2573586, 21584425, 181223408, 1522659737, 12799736142, 107631298349, 905250578212, 7614837072565, 64060941839946, 538955843348689, 4534517540404184, 38152320928270193, 321010168596786054

Offset: 0

Author

Klaus Brockhaus, Jul 28 2009

Keywords

• nonn

Comments

Binomial transform of A163458. Inverse binomial transform of A163460.

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. A163458, A163460.

Programs

Magma

[ n le 2 select 7*n-6 else 14*Self(n-1)-47*Self(n-2): n in [1..20] ];

Mathematica

LinearRecurrence[{14, -47}, {1, 8}, 50] (* G. C. Greubel, Dec 24 2016 *)

PARI

Vec((1-6*x)/(1-14*x+47*x^2) + O(x^50)) \\ G. C. Greubel, Dec 24 2016

Formula

a(n) = ((2+sqrt(2))*(7+sqrt(2))^n + (2-sqrt(2))*(7-sqrt(2))^n)/4.

G.f.: (1-6*x)/(1-14*x+47*x^2).

E.g.f.: (1/2)*exp(7*x)*(sqrt(2)*sinh(sqrt(2)*x) + 2*cosh(sqrt(2)*x)). - G. C. Greubel, Dec 24 2016