A053428 a(n) = a(n-1) + 20*a(n-2), n >= 2; a(0)=1, a(1)=1.

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

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

Cf. A001045, A015441, A053404, A000302, A053573, A080424.

Sequence in context: A147273 A195034 A067344 * A123842 A247387 A362849

Adjacent sequences: A053425 A053426 A053427 * A053429 A053430 A053431

Keyword

easy,nonn

Author

Barry E. Williams, Jan 10 2000

Extensions

More terms from James A. Sellers, Feb 02 2000

Status

approved