

A093103


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


2



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

1,2


COMMENTS

a(n+1)/a(n) converges to 4+sqrt(37).


LINKS

Table of n, a(n) for n=1..19.
Index entries for linear recurrences with constant coefficients, signature (8, 21).


FORMULA

a(n)=(1/2)*[4sqrt(37)]^n+(2/37)*sqrt(37)*[4+sqrt(37)]^n+(1/2)*[4+sqrt(37)]^n(2/37)*[4 sqrt(37)]^n*sqrt(37), with n>=0  Paolo P. Lava, Jul 08 2008
G.f.: x/(18x21x^2). [From R. J. Mathar, Nov 30 2008]


MATHEMATICA

Join[{b=1}, a=0; Table[c=8*b+21*a; a=b; b=c, {n, 30}]] (* Vladimir Joseph Stephan Orlovsky, Apr 22 2011 *)
LinearRecurrence[{8, 21}, {1, 8}, 20] (* Harvey P. Dale, Jan 14 2012 *)


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



