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Search: id:A164541
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| A164541 |
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a(n) = ((1+3*sqrt(2))*(3+2*sqrt(2))^n+(1-3*sqrt(2))*(3-2*sqrt(2))^n)/2. |
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+0
3
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| 1, 15, 89, 519, 3025, 17631, 102761, 598935, 3490849, 20346159, 118586105, 691170471, 4028436721, 23479449855, 136848262409, 797610124599, 4648812485185, 27095264786511, 157922776233881, 920441392616775
(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 A164540. Third binomial transform of A164675. Inverse binomial transform of A164542.
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FORMULA
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a(n) = 6*a(n-1)-a(n-2) for n > 1; a(0) = 1, a(1) = 15.
G.f: (1+9*x)/(1-6*x+x^2).
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PROGRAM
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(MAGMA) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((1+3*r)*(3+2*r)^n+(1-3*r)*(3-2*r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Aug 20 2009]
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CROSSREFS
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Cf. A164540, A164675, A164542.
Sequence in context: A091286 A064058 A138322 this_sequence A145789 A010822 A022707
Adjacent sequences: A164538 A164539 A164540 this_sequence A164542 A164543 A164544
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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 15 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 20 2009
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