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Search: id:A147518
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| A147518 |
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Expansion of (1-x)/(1-4*x-6*x^2). |
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+0
1
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| 1, 3, 18, 90, 468, 2412, 12456, 64296, 331920, 1713456, 8845344, 45662112, 235720512, 1216854720, 6281741952, 32428096128, 167402836224, 864179921664, 4461136704000, 23029626345984, 118885325607936, 613719060507648
(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 [1,2,13,44,205,...] = A002534(n+1).
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FORMULA
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a(n)=4*a(n-1)+6*a(n-2); a(0)=1, a(1)=3. a(n)=Sum_{k, 0<=k<=n}A122016(n,k)*3^k.
a(n)=(1/2)*[2+sqrt(10)]^n-(1/20)*[2-sqrt(10)]^n*sqrt(10)+(1/20)*[2+sqrt(10)]^n*sqrt(10)+(1/2) *[2-sqrt(10)]^n, with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Nov 18 2008]
a(n)= ((10+sqrt(10))/20)*(2+sqrt(10))^n+((10-sqrt(10))/20)*(2-sqrt(10))^n [From Richard Choulet (richardchoulet(AT)yahoo.fr), Nov 20 2008]
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CROSSREFS
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Cf. A026150, A122117
Sequence in context: A037295 A124811 A006568 this_sequence A088336 A133594 A092691
Adjacent sequences: A147515 A147516 A147517 this_sequence A147519 A147520 A147521
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KEYWORD
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nonn
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AUTHOR
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Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 06 2008
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