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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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified October 16 06:10 EDT 2019. Contains 328046 sequences. (Running on oeis4.)