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Search: id:A053428
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| A053428 |
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A second order recurrence. |
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+0
4
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| 1, 1, 21, 41, 461, 1281, 10501, 36121, 246141, 968561, 5891381, 25262601, 143090221, 648342241, 3510146661, 16476991481, 86679924701, 416219754321, 2149818248341, 10474213334761, 53470578301581, 262954844996801
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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a(n)=a(n-1)+20a(n-2), n>1; a(0)=1, a(1)=1.
Hankel transform is := 1,20,0,0,0,0,0,0,0,0,0,0,... [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 02 2008]
Diagonals of triangle: A038207 [From M. Dols (markdols99(AT)yahoo.com), Aug 31 2009]
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REFERENCES
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A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
A. K. Whitford, Binet's Formula Generalized, Fibonacci Quarterly, Vol. 15, No. 1, 1979, pp. 21,24,29.
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FORMULA
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a(n)=[(5^(n+1))-(-4)^(n+1)]/9.
G.f.: -1/(4*x+1)/(5*x-1). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 16 2007
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CROSSREFS
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Cf. A001045, A015441, A053404.
Sequence in context: A154576 A147273 A067344 this_sequence A123842 A120772 A040420
Adjacent sequences: A053425 A053426 A053427 this_sequence A053429 A053430 A053431
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KEYWORD
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easy,nonn
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AUTHOR
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Barry E. Williams, Jan 10 2000
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Feb 02 2000
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