A163307 a(n) = 14*a(n-1) - 44*a(n-2) for n > 1; a(0) = 1, a(1) = 8.

1, 8, 68, 600, 5408, 49312, 452416, 4164096, 38391040, 354254336, 3270354944, 30197778432, 278873280512, 2575523676160, 23786907123712, 219693657980928, 2029087298289664, 18740701224894464, 173089976023777280

Offset

0,2

Comments

Binomial transform of A163306. Inverse binomial transform of A163308.

Links

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

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

Formula

a(n) = ((5+sqrt(5))*(7+sqrt(5))^n + (5-sqrt(5))*(7-sqrt(5))^n)/10.

G.f.: (1-6*x)/(1-14*x+44*x^2).

E.g.f.: (1/5)*exp(7*x)*(5*cosh(sqrt(5)*x) + sqrt(5)*sinh(sqrt(5)*x)). - G. C. Greubel, Dec 18 2016

Mathematica

LinearRecurrence[{14, -44}, {1, 8}, 50] (* G. C. Greubel, Dec 18 2016 *)

Prog

(Magma) [ n le 2 select 7*n-6 else 14*Self(n-1)-44*Self(n-2): n in [1..19] ];
(PARI) Vec((1-6*x)/(1-14*x+44*x^2) + O(x^50)) \\ G. C. Greubel, Dec 18 2016

Crossrefs

Cf. A163306, A163308.

Sequence in context: A249390 A190510 A282563 * A281337 A152105 A068766

Adjacent sequences: A163304 A163305 A163306 * A163308 A163309 A163310

Keyword

nonn

Author

Klaus Brockhaus, Jul 24 2009

Status

approved