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

0,2

Comments

Eighth binomial transform of A108411. Binomial transform of A162758.

Links

Table of n, a(n) for n=0..18.

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

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).

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A037502 A037679 A015579 * A147960 A155499 A321294

Adjacent sequences: A162756 A162757 A162758 * A162760 A162761 A162762

Keyword

nonn

Author

Klaus Brockhaus, Jul 13 2009

Status

approved