A162759 a(n) = 16*a(n-1)-61*a(n-2) for n > 1; a(0) = 1, a(1) = 9.

1, 9, 83, 779, 7401, 70897, 682891, 6601539, 63968273, 620798489, 6030711171, 58622670907, 570089353081, 5545446723969, 53951697045563, 524954902566899, 5108224921291041, 49709349684075817, 483747874746459571

Offset: 0

Author

Klaus Brockhaus, Jul 13 2009

Keywords

• nonn

Comments

Eighth binomial transform of A108411. Binomial transform of A162758.

Links

• Index entries for linear recurrences with constant coefficients, signature (16, -61).

Crossrefs

Cf. A108411 (powers of 3 repeated), A162758.

Programs

Magma

[ n le 2 select 8*n-7 else 16*Self(n-1)-61*Self(n-2): n in [1..19] ];

Mathematica

LinearRecurrence[{16,-61},{1,9},30] (* Harvey P. Dale, Jan 18 2014 *)

Formula

a(n) = ((3+sqrt(3))*(8+sqrt(3))^n+(3-sqrt(3))*(8-sqrt(3))^n)/6.

G.f.: (1-7*x)/(1-16*x+61*x^2).