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A092164
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Let M = 2 X 2 matrix [ 1 2 / 5 4 ]; a(n) = (1,1) entry of M^n.
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3
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1, 11, 61, 371, 2221, 13331, 79981, 479891, 2879341, 17276051, 103656301, 621937811, 3731626861, 22389761171, 134338567021, 806031402131, 4836188412781, 29017130476691, 174102782860141, 1044616697160851
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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FORMULA
| a(n) = (2*6^n + 5*(-1)^n)/7.
A092165 +(-1)^n.
a(n)=5*a(n-1)+6*a(n-2). G.f.: x*(1+6*x)/((1+x)*(1-6*x)). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 20 2009]
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MATHEMATICA
| Table[ MatrixPower[{{1, 2}, {5, 4}}, n][[1, 1]], {n, 20}] (from Robert G. Wilson v Apr 22 2004)
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CROSSREFS
| Cf. A092165, A092166, A092167.
Sequence in context: A199414 A156095 A068846 * A088545 A020454 A009016
Adjacent sequences: A092161 A092162 A092163 * A092165 A092166 A092167
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KEYWORD
| nonn
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AUTHOR
| Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Apr 01 2004
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EXTENSIONS
| Edited by Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 22 2004
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