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a(1)=2, a(2)=5, a(n)=2*a(n-1) + 5*a(n-2).
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%I #30 Dec 31 2023 10:23:10

%S 2,5,20,65,230,785,2720,9365,32330,111485,384620,1326665,4576430,

%T 15786185,54454520,187839965,647952530,2235104885,7709972420,

%U 26595469265,91740800630,316458947585,1091621898320,3765538534565,12989186560730,44806065794285

%N a(1)=2, a(2)=5, a(n)=2*a(n-1) + 5*a(n-2).

%H Vincenzo Librandi, <a href="/A189734/b189734.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 (2,5).

%F G.f.: x*(2+x)/(1-2*x-5*x^2). - _Bruno Berselli_, May 24 2011

%t LinearRecurrence[{2,5},{2,5},40]

%o (Maxima) a[1]:2$ a[2]:5$ a[n]:=2*a[n-1]+5*a[n-2]$ makelist(a[n], n, 1, 26); /* _Bruno Berselli_, May 24 2011 */

%Y Cf. A000045, A000079, A105476, A159612, A080040, A135522, A103435, A189732, A189735, A189736, A189737, A189738, A189739, A189741, A189742, A189743, A189744, A189745, A189746, A189747, A189748, A189749.

%K nonn

%O 1,1

%A _Harvey P. Dale_, Apr 26 2011