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
Vincenzo Librandi, Table of n, a(n) for n = 0..400
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.
Index entries for linear recurrences with constant coefficients, signature (1,20).
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