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

Author

Barry E. Williams, Jan 10 2000

Keywords

• easy
• nonn

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).

Crossrefs

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

Programs

Magma

[((5^(n+1))-(-4)^(n+1)) div 9: n in [0..40]]; // Vincenzo Librandi, Jun 07 2011

Mathematica

Join[{a=1,b=1},Table[c=b+20*a;a=b;b=c,{n,60}]] (* Vladimir Joseph Stephan Orlovsky, Feb 01 2011 *)

PARI

a(n)=((5^(n+1))-(-4)^(n+1))/9 \\ Charles R Greathouse IV, Jun 10 2011

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

Extensions

More terms from James Sellers, Feb 02 2000