A163460 a(n) = 16*a(n-1) - 62*a(n-2) for n > 1; a(0) = 1, a(1) = 9.

1, 9, 82, 754, 6980, 64932, 606152, 5672648, 53180944, 499190928, 4689836320, 44087543584, 414630845504, 3900665825856, 36703540792448, 345415371476096, 3251026414485760, 30600669600254208, 288047075905950208

Offset

0,2

Comments

Binomial transform of A163459. Inverse binomial transform of A163461.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (16, -62).

Formula

a(n) = ((2+sqrt(2))*(8+sqrt(2))^n + (2-sqrt(2))*(8-sqrt(2))^n)/4.

G.f.: (1-7*x)/(1-16*x+62*x^2).

E.g.f.: (1/2)*exp(8*x)*(2*cosh(sqrt(2)*x) + sqrt(2)*sinh(sqrt(2)*x)). - G. C. Greubel, Dec 24 2016

Mathematica

LinearRecurrence[{16, -62}, {1, 9}, 30] (* Harvey P. Dale, Jul 13 2014 *)

Prog

(Magma) [ n le 2 select 8*n-7 else 16*Self(n-1)-62*Self(n-2): n in [1..19] ];
(PARI) Vec((1-7*x)/(1-16*x+62*x^2) + O(x^50)) \\ G. C. Greubel, Dec 24 2016

Crossrefs

Cf. A163459, A163461.

Sequence in context: A099371 A334611 A068109 * A081191 A060531 A248848

Adjacent sequences: A163457 A163458 A163459 * A163461 A163462 A163463

Keyword

nonn

Author

Klaus Brockhaus, Jul 28 2009

Status

approved