|
%I
%S 1,5,10,35,85,260,685,1985,5410,15335,42385,119060,330985,926285,
%T 2581210,7212635,20118685,56181860,156775285,437684585,1221561010,
%U 3409983935,9517788985,26567708660,74156653585,206995196885,577778464810,1612754449235,4501646773285
%N a(1)=1, a(2)=5, a(n)=a(n-1) + 5a(n-2).
%H Vincenzo Librandi, <a href="/A189732/b189732.txt">Table of n, a(n) for n = 1..100</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1, 5).
%F a(n) = 1/2*((1/2+1/2*sqrt(21))^(n-1)+(1/2-1/2*sqrt(21))^(n-1)+3/14*sqrt(21)*((1/2+1/2 *sqrt(21))^(n-1)-(1/2-1/2*sqrt(21))^(n-1)). - Paolo P. Lava, May 24 2011
%F G.f.: x*(1+4*x)/(1-x-5*x^2). - Bruno Berselli, May 24 2011
%F a(n+1) = Sum_{k, 0<=k<=n} A119473(n,k)*4^k. - _Philippe Deléham_, Oct 05 2012
%t LinearRecurrence[{1,5},{1,5},40]
%o (Maxima) a[1]:1$ a[2]:5$ a[n]:=a[n-1]+5*a[n-2]$ makelist(a[n], n, 1, 29); [Bruno Berselli, May 24 2011]
%Y Cf. A000045, A000079, A105476, A159612, A080040, A135522, A103435, A189734, A189735, A189736, A189737, A189738, A189739, A189741, A189742,A189743, A189744, A189745, A189746, A189747, A189748, A189749.
%K nonn
%O 1,2
%A _Harvey P. Dale_, Apr 26 2011
|
