A093103 a(n+2) = 8*a(n+1) + 21*a(n), with a(1)=1, a(2)=8.

1, 8, 85, 848, 8569, 86360, 870829, 8780192, 88528945, 892615592, 9000032581, 90745188080, 914962188841, 9225346460408, 93016977648925, 937868096859968, 9456301305507169, 95345640478116680, 961347451240583989

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..990

Index entries for linear recurrences with constant coefficients, signature (8,21).

Formula

Limit_{n -> oo} a(n+1)/a(n) converges to 4 + sqrt(37).

G.f.: x/(1-8*x-21*x^2). - R. J. Mathar, Nov 30 2008

a(n) = (i*sqrt(21))^n * ChebyshevU(n, -4*i/sqrt(21)). - G. C. Greubel, Feb 09 2023

Mathematica

LinearRecurrence[{8, 21}, {1, 8}, 40] (* Harvey P. Dale, Jan 14 2012 *)

Prog

(Magma) [n le 2 select 7*n-6 else 8*Self(n-1) +21*Self(n-2): n in [1..41]]; // G. C. Greubel, Feb 09 2023
(SageMath)
@CachedFunction
def a(n): # a = A093103
    if (n<3): return 7*n-6
    else: return 8*a(n-1) + 21*a(n-2)
[a(n) for n in range(1, 41)] # G. C. Greubel, Feb 09 2023

Crossrefs

Cf. A093117, A094703.

Sequence in context: A281340 A298283 A299176 * A288691 A300675 A241323

Adjacent sequences: A093100 A093101 A093102 * A093104 A093105 A093106

Keyword

nonn

Author

Gary W. Adamson, May 20 2004

Extensions

More terms from Robert G. Wilson v, May 24 2004

Edited by Don Reble, Nov 04 2005

Status

approved