A190005 a(n) = 6*a(n-1) + 10*a(n-2), with a(0)=0, a(1)=1.

0, 1, 6, 46, 336, 2476, 18216, 134056, 986496, 7259536, 53422176, 393128416, 2892992256, 21289237696, 156665348736, 1152884469376, 8483960303616, 62432606515456, 459435242128896, 3380937517927936, 24879977528856576, 183089240352418816, 1347335217403078656

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (6,10).

Formula

a(n) = sqrt(19)*((3+sqrt(19))^n - (3-sqrt(19))^n)/38. - Paolo P. Lava, Jun 06 2011

G.f.: x/(1 - 6*x - 10*x^2). - R. J. Mathar, Nov 20 2011

Mathematica

LinearRecurrence[{6, 10}, {0, 1}, 50]
CoefficientList[Series[x/(1-6*x-10*x^2), {x, 0, 50}], x] (* G. C. Greubel, Jan 11 2018 *)

Prog

(PARI) x='x+O('x^30); concat([0], Vec(x/(1-6*x-10*x^2))) \\ G. C. Greubel, Jan 11 2018
(Magma) I:=[0, 1]; [n le 2 select I[n] else 6*Self(n-1) + 10*Self(n-2): n in [1..30]]; \\ G. C. Greubel, Jan 11 2018

Crossrefs

Sequence in context: A240779 A073507 A155598 * A334609 A253654 A301421

Adjacent sequences: A190002 A190003 A190004 * A190006 A190007 A190008

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, May 24 2011

Status

approved