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A053428
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a(n) = a(n-1)+20*a(n-2), n>=2; a(0)=1, a(1)=1.
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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; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| 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]
Zero followed with this sequence is the inverse binomial transform of A080424. - Paul Curtz, Jun 07 2011
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REFERENCES
| 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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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..400
Index entries for sequences related to linear recurrences with constant coefficients, signature (1,20).
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FORMULA
| a(n) = ((5^(n+1))-(-4)^(n+1))/9.
G.f.: 1/(1+4*x)/(1-5*x). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 16 2007
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MATHEMATICA
| Join[{a=1, b=1}, Table[c=b+20*a; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Feb 01 2011 *)
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PROG
| (MAGMA) [((5^(n+1))-(-4)^(n+1)) div 9: n in [0..40]]; // Vincenzo Librandi, Jun 07 2011
(PARI) a(n)=((5^(n+1))-(-4)^(n+1))/9 \\ Charles R Greathouse IV, Jun 10 2011
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CROSSREFS
| Cf. A001045, A015441, A053404, A000302, A053573, A080424.
Sequence in context: A147273 A195034 A067344 * A123842 A120772 A040420
Adjacent sequences: A053425 A053426 A053427 * A053429 A053430 A053431
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KEYWORD
| easy,nonn
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AUTHOR
| Barry E. Williams, Jan 10 2000
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Feb 02 2000
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