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Search: id:A164031
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| A164031 |
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a(n) = ((2+3*sqrt(2))*(5+sqrt(2))^n+(2-3*sqrt(2))*(5-sqrt(2))^n)/4. |
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+0
3
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| 1, 8, 57, 386, 2549, 16612, 107493, 692854, 4456201, 28626368, 183771057, 1179304106, 7566306749, 48539073052, 311365675293, 1997258072734, 12811170195601, 82174766283128, 527090748332457, 3380887858812626
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Binomial transform of A164072. Fifth binomial transform of A164073.
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FORMULA
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a(n) = 10*a(n-1)-23*a(n-2) for n > 1; a(0) = 1, a(1) = 8.
G.f.: (1-2*x)/(1-10*x+23*x^2).
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PROGRAM
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(MAGMA) Z<x>:= PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((2+3*r)*(5+r)^n+(2-3*r)*(5-r)^n)/4: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Aug 09 2009]
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CROSSREFS
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Cf. A164072, A164073 (1, 3, 2, 6, 4, 12).
Sequence in context: A096711 A079926 A108666 this_sequence A023000 A097114 A022038
Adjacent sequences: A164028 A164029 A164030 this_sequence A164032 A164033 A164034
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KEYWORD
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nonn
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AUTHOR
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Al Hakanson (hawkuu(AT)gmail.com), Aug 08 2009
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EXTENSIONS
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Edited and extended beyond a(5) by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Aug 09 2009
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