A163307 a(n) = 14*a(n-1) - 44*a(n-2) for n > 1; a(0) = 1, a(1) = 8.

1, 8, 68, 600, 5408, 49312, 452416, 4164096, 38391040, 354254336, 3270354944, 30197778432, 278873280512, 2575523676160, 23786907123712, 219693657980928, 2029087298289664, 18740701224894464, 173089976023777280

Offset: 0

Author

Klaus Brockhaus, Jul 24 2009

Keywords

• nonn

Comments

Binomial transform of A163306. Inverse binomial transform of A163308.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (14,-44).

Crossrefs

Cf. A163306, A163308.

Programs

Magma

[ n le 2 select 7*n-6 else 14*Self(n-1)-44*Self(n-2): n in [1..19] ];

Mathematica

LinearRecurrence[{14,-44}, {1,8}, 50] (* G. C. Greubel, Dec 18 2016 *)

PARI

Vec((1-6*x)/(1-14*x+44*x^2) + O(x^50)) \\ G. C. Greubel, Dec 18 2016

Formula

a(n) = ((5+sqrt(5))*(7+sqrt(5))^n + (5-sqrt(5))*(7-sqrt(5))^n)/10.

G.f.: (1-6*x)/(1-14*x+44*x^2).

E.g.f.: (1/5)*exp(7*x)*(5*cosh(sqrt(5)*x) + sqrt(5)*sinh(sqrt(5)*x)). - G. C. Greubel, Dec 18 2016