%I #22 Sep 08 2022 08:45:54
%S 1,3,13,49,186,711,2749,10705,41946,165159,652765,2587441,10278906,
%T 40903047,162974461,649984657,2594199066,10359577575,41386654237,
%U 165391648753,661101690426,2643012047943,10567864050493,42258903778129
%N a(n) = floor((3*4^n + 2*3^n)/5).
%F a(n) = 7*a(n-1) - 12*a(n-2) + a(n-4) - 7*a(n-5) + 12*a(n-6); initial terms are 1, 3, 13, 49, 186, 711.
%F a(n) = 6*a(n-1) - 6*a(n-2) - 6*a(n-3) - 5*a(n-4) - 12*a(n-5) - 6; initial terms are 1, 3, 13, 49, 186.
%F G.f.: (1-4*x+4*x^2-6*x^3-2*x^4+x^5)/((1-3*x)*(1-4*x)*(1-x^4)).
%o (Maxima) makelist(floor((3*4^n+2*3^n)/5),n,0,12);
%o (Magma) [ (3*4^n+2*3^n) div 5: n in [0..30] ]; // _Vincenzo Librandi_, Dec 31 2010
%o (PARI) a(n) = (3*4^n + 2*3^n)\5 \\ _Michel Marcus_, Apr 24 2018
%Y Cf. A178935, A178936.
%K nonn,easy
%O 0,2
%A _Emanuele Munarini_, Dec 30 2010