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A164592
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a(n) = 10*a(n-1)-17*a(n-2) for n > 1; a(0) = 1, a(1) = 8.
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2
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1, 8, 63, 494, 3869, 30292, 237147, 1856506, 14533561, 113775008, 890679543, 6972620294, 54584650709, 427311962092, 3345180558867, 26187502233106, 205006952830321, 1604881990340408, 12563701705288623, 98354023217099294, 769957303181086349
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Binomial transform of A164591. Fifth binomial transform of A096886.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..144
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FORMULA
| a(n) = 10*a(n-1)-17*a(n-2) for n > 1; a(0) = 1, a(1) = 8.
a(n) = ((4 + sqrt(18))*(5 + sqrt(8))^n + (4 - sqrt(18))*(5 - sqrt(8))^n)/8
G.f.:(1-2*x)/(1-10*x+17*x^2).
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MATHEMATICA
| CoefficientList[Series[(1 - 2*z)/(17*z^2 - 10*z + 1), {z, 0, 200}], z] (* From Vladimir Joseph Stephan Orlovsky, Jun 12 2011 *)
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PROG
| (MAGMA) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((4+3*r)*(5+2*r)^n+(4-3*r)*(5-2*r)^n)/8: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Aug 24 2009]
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CROSSREFS
| Cf. A164591, A096886.
Sequence in context: A085433 A171313 A081107 * A001090 A105219 A060071
Adjacent sequences: A164589 A164590 A164591 * A164593 A164594 A164595
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KEYWORD
| nonn,easy
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AUTHOR
| Al Hakanson (hawkuu(AT)gmail.com), Aug 17 2009
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EXTENSIONS
| Extended by Klaus Brockhaus and R. J. Mathar Aug 24 2009
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