A163147 a(n) = 14*a(n-1) - 44*a(n-2) for n > 1; a(0) = 1, a(1) = 12.

1, 12, 124, 1208, 11456, 107232, 997184, 9242368, 85517056, 790574592, 7305293824, 67488831488, 623410712576, 5758241390592, 53185308114944, 491231692423168, 4537090136866816, 41905067449516032, 387038978271084544

Offset: 0

Author

Klaus Brockhaus, Jul 21 2009

Keywords

• nonn

Comments

Binomial transform of A163146. Inverse binomial transform of A163148.

Links

• Index entries for linear recurrences with constant coefficients, signature (14,-44).

Crossrefs

Cf. A163146, A163148.

Programs

Magma

[ n le 2 select 11*n-10 else 14*Self(n-1)-44*Self(n-2): n in [1..19] ];

PARI

Vec((1-2*x)/(1-14*x+44*x^2) + O(x^30)) \\ Jinyuan Wang, Mar 23 2020

Formula

a(n) = ((1+sqrt(5))*(7+sqrt(5))^n+(1-sqrt(5))*(7-sqrt(5))^n)/2.

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