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

%I A053428 #42 Jul 02 2025 16:01:59
%S A053428 1,1,21,41,461,1281,10501,36121,246141,968561,5891381,25262601,
%T A053428 143090221,648342241,3510146661,16476991481,86679924701,416219754321,
%U A053428 2149818248341,10474213334761,53470578301581,262954844996801
%N A053428 a(n) = a(n-1) + 20*a(n-2), n >= 2; a(0)=1, a(1)=1.
%C A053428 Hankel transform is 1,20,0,0,0,0,0,0,0,0,0,0,... - _Philippe Deléham_, Nov 02 2008
%C A053428 Zero followed by this sequence gives the inverse binomial transform of A080424. - _Paul Curtz_, Jun 07 2011
%D A053428 A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
%H A053428 Vincenzo Librandi, <a href="/A053428/b053428.txt">Table of n, a(n) for n = 0..400</a>
%H A053428 F. P. Muga II, <a href="https://www.researchgate.net/publication/267327689">Extending the Golden Ratio and the Binet-de Moivre Formula</a>, March 2014; Preprint on ResearchGate.
%H A053428 A. K. Whitford, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/15-1/whitford-a.pdf">Binet's Formula Generalized</a>, Fibonacci Quarterly, Vol. 15, No. 1, 1979, pp. 21, 24, 29.
%H A053428 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,20).
%F A053428 a(n) = ((5^(n+1)) - (-4)^(n+1))/9.
%F A053428 G.f.: 1/((1+4*x)*(1-5*x)). - _R. J. Mathar_, Nov 16 2007
%t A053428 Join[{a=1,b=1},Table[c=b+20*a;a=b;b=c,{n,60}]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 01 2011 *)
%o A053428 (Magma) [((5^(n+1))-(-4)^(n+1)) div 9: n in [0..40]]; // _Vincenzo Librandi_, Jun 07 2011
%o A053428 (PARI) a(n)=((5^(n+1))-(-4)^(n+1))/9 \\ _Charles R Greathouse IV_, Jun 10 2011
%Y A053428 Cf. A001045, A015441, A053404, A000302, A053573, A080424.
%K A053428 easy,nonn
%O A053428 0,3
%A A053428 _Barry E. Williams_, Jan 10 2000
%E A053428 More terms from _James Sellers_, Feb 02 2000