A162758 a(n) = 14*a(n-1)-46*a(n-2) for n > 1; a(0) = 1, a(1) = 8.

1, 8, 66, 556, 4748, 40896, 354136, 3076688, 26783376, 233439616, 2036119328, 17767448256, 155082786496, 1353856391168, 11820181297536, 103205144171776, 901143678718208, 7868574870153216, 68707438961107456, 599949701428456448

Offset: 0

Author

Klaus Brockhaus, Jul 13 2009

Keywords

• nonn

Comments

Seventh binomial transform of A108411. Binomial transform of A162757. Inverse binomial transform of A162759.

Links

• Index entries for linear recurrences with constant coefficients, signature (14, -46).

Crossrefs

Cf. A108411 (powers of 3 repeated), A162757, A162759.

Programs

Magma

[ n le 2 select 7*n-6 else 14*Self(n-1)-46*Self(n-2): n in [1..20] ];

Mathematica

LinearRecurrence[{14,-46},{1,8},30] (* Harvey P. Dale, Apr 09 2012 *)

Formula

a(n) = ((3+sqrt(3))*(7+sqrt(3))^n+(3-sqrt(3))*(7-sqrt(3))^n)/6.

G.f.: (1-6*x)/(1-14*x+46*x^2).