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A053428
a(n) = a(n-1) + 20*a(n-2), n >= 2; a(0)=1, a(1)=1.
7
1, 1, 21, 41, 461, 1281, 10501, 36121, 246141, 968561, 5891381, 25262601, 143090221, 648342241, 3510146661, 16476991481, 86679924701, 416219754321, 2149818248341, 10474213334761, 53470578301581, 262954844996801
OFFSET
0,3
COMMENTS
Hankel transform is 1,20,0,0,0,0,0,0,0,0,0,0,... - Philippe Deléham, Nov 02 2008
Zero followed by this sequence gives the inverse binomial transform of A080424. - Paul Curtz, Jun 07 2011
REFERENCES
A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
LINKS
F. P. Muga II, Extending the Golden Ratio and the Binet-de Moivre Formula, March 2014; Preprint on ResearchGate.
A. K. Whitford, Binet's Formula Generalized, Fibonacci Quarterly, Vol. 15, No. 1, 1979, pp. 21, 24, 29.
FORMULA
a(n) = ((5^(n+1)) - (-4)^(n+1))/9.
G.f.: 1/((1+4*x)*(1-5*x)). - R. J. Mathar, Nov 16 2007
MATHEMATICA
Join[{a=1, b=1}, Table[c=b+20*a; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Feb 01 2011 *)
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
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Barry E. Williams, Jan 10 2000
EXTENSIONS
More terms from James A. Sellers, Feb 02 2000
STATUS
approved