%I #13 May 30 2020 10:54:07
%S 1,2,15,58,239,954,3823,15290,61167,244666,978671,3914682,15658735,
%T 62634938,250539759,1002159034,4008636143,16034544570,64138178287,
%U 256552713146,1026210852591,4104843410362,16419373641455,65677494565818
%N a(0)=1, a(1)=2; for n>1, a(n)=3*a(n-1)+4*a(n-2)+5.
%C First prime terms are a(n) with a = 1, 4, 6, 18, 88.
%F a(n) = (28*4^n + 27(-1)^n - 25)/30.
%F G.f. = (1 - 2*x + 6*x^2)/(1 - 4*x - x^2 + 4*x^3).
%t RecurrenceTable[{a[0]==1,a[1]==2,a[n]==3a[n-1]+4a[n-2]+5},a,{n,30}] (* _Harvey P. Dale_, May 30 2020 *)
%o (Sage)
%o from sage.combinat.sloane_functions import recur_gen2b
%o it = recur_gen2b(1,2,3,4, lambda n: 5)
%o [next(it) for i in range(24)] # _Zerinvary Lajos_, Jul 16 2008
%K nonn
%O 0,2
%A _Zak Seidov_, Feb 26 2007
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