

A053428


a(n) = a(n1) + 20*a(n2), 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
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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. 194196.


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..400
F. P. Muga II, Extending the Golden Ratio and the Binetde 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)*(15*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 A120772
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



