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A093103
a(n+2) = 8*a(n+1) + 21*a(n), with a(1)=1, a(2)=8.
3
1, 8, 85, 848, 8569, 86360, 870829, 8780192, 88528945, 892615592, 9000032581, 90745188080, 914962188841, 9225346460408, 93016977648925, 937868096859968, 9456301305507169, 95345640478116680, 961347451240583989
OFFSET
1,2
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
Sequence in context: A281340 A298283 A299176 * A288691 A300675 A241323
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