A158797 a(n) = a(n-1) + 36*a(n-2), a(0)=1, a(1)=6.

1, 6, 42, 258, 1770, 11058, 74778, 472866, 3164874, 20188050, 134123514, 860893314, 5689339818, 36681499122, 241497732570, 1562031700962, 10255950073482, 66489091308114, 435703293953466, 2829310581045570

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (1,36).

Formula

G.f.: (1+5*x)/(1-x-36*x^2).

a(n) = (6*i)^n*( ChebyshevU(n, -i/12) - (5*i/6)*ChebyshevU(n-1, -i/12) ). - G. C. Greubel, Dec 22 2021

Mathematica

LinearRecurrence[{1, 36}, {1, 6}, 30] (* Harvey P. Dale, Apr 30 2013 *)

Prog

(PARI) Vec((1+5*x)/(1-x-36*x^2)+O(x^99)) \\ Charles R Greathouse IV, Jan 17 2012
(Sage) [(6*i)^n*( chebyshev_U(n, -i/12) - (5*i/6)*chebyshev_U(n-1, -i/12) ) for n in (0..40)] # G. C. Greubel, Dec 22 2021
(Magma) I:=[1, 6]; [n le 2 select I[n] else Self(n-1) + 36*Self(n-2): n in [1..41]]; // G. C. Greubel, Dec 22 2021

Crossrefs

Cf. A000045, A026597, A122994, A122995, A158608.

Sequence in context: A180355 A105281 A246938 * A218060 A283328 A343363

Adjacent sequences: A158794 A158795 A158796 * A158798 A158799 A158800

Keyword

nonn,easy,less

Author

Philippe Deléham, Mar 27 2009

Status

approved