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

Author

Philippe Deléham, Mar 27 2009

Keywords

• nonn
• easy
• less

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,36).

Crossrefs

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

Programs

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

Mathematica

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

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

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