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Search: id:A143079
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| A143079 |
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((9+sqrt9)^n+(9-sqrt9)^n)/2. |
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+0
4
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| 1, 9, 90, 972, 11016, 128304, 1516320, 18055872, 215830656, 2584929024, 30988915200, 371685583872, 4459138615296, 53503133036544, 641998414356480, 7703745879785472, 92443540002471936, 1109314016699940864
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Equals A007318^9 * [1, 0, 9, 0, 81, 0, 729,...]. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 23 2008]
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FORMULA
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a(n)=18*a(n-1)-72*a(n-2). a(n)=6^n*(2^n+1)/2 . G.f.:(1-9x)/(1-18x+72x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 18 2008]
a(n)=(12^n+6^n)/2. G.f.: (1-9x)/((1-12x)(1-6x)). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 21 2008]
a(n) = 3^n*A007582(n) = (6^n+12^n)/2 = A000051(n)*A000079(n)*A000244(n)/2. [From M. F. Hasler (MHasler(AT)univ-ag.fr), Oct 22 2008]
A007318^9 * [1, 0, 9, 0, 81, 0, 729...] produces this sequence. - Gary Adamson, Oct 23 2008
a(n)=Sum_{k, 0<=k<=n}A098158(n,k)*9^k. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 23 2008]
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EXAMPLE
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a(3)=972
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PROGRAM
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(PARI) A143079(n)=3^n*(1+1<<n)<<(n-1) [From M. F. Hasler (MHasler(AT)univ-ag.fr), Oct 22 2008]
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CROSSREFS
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Sequence in context: A147841 A036258 A098399 this_sequence A165324 A082367 A049389
Adjacent sequences: A143076 A143077 A143078 this_sequence A143080 A143081 A143082
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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), Oct 15 2008
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EXTENSIONS
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Extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl) and M. F. Hasler (MHasler(AT)univ-ag.fr), Oct 21 2008
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