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A163346
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a(n) = ((1+sqrt(2))*(5+sqrt(2))^n+(1-sqrt(2))*(5-sqrt(2))^n)/2.
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3
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1, 7, 47, 309, 2009, 12983, 83623, 537621, 3452881, 22163527, 142219007, 912428949, 5853252329, 37546657463, 240841771063, 1544844588981, 9909085155361, 63559426007047, 407685301497167, 2614986216809589
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Binomial transform of A163350. Fifth binomial transform of A163403.
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FORMULA
| a(n) = 10*a(n-1)-23*a(n-2) for n > 1; a(0) = 1, a(1) = 7.
G.f.: (1-3*x)/(1-10*x+23*x^2).
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PROG
| (MAGMA) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((1+r)*(5+r)^n+(1-r)*(5-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jul 26 2009]
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CROSSREFS
| Cf. A163350, A163403.
Sequence in context: A126635 A085352 A125370 * A186446 A126528 A098405
Adjacent sequences: A163343 A163344 A163345 * A163347 A163348 A163349
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KEYWORD
| nonn
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AUTHOR
| Al Hakanson (hawkuu(AT)gmail.com), Jul 25 2009
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EXTENSIONS
| Edited and extended beyond a(5) by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jul 26 2009
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