A375320 - OEIS

%I #7 Aug 12 2024 09:34:47

%S 1,1,0,1,5,10,11,14,37,85,139,204,371,768,1432,2398,4117,7685,14422,

%T 25744,45037,80888,148408,269402,480873,859580,1554254,2817518,

%U 5074004,9103828,16384908,29588793,53381548,96068570,172864927,311535484,561770980,1012168575

%N Expansion of (1 + x)/(1 - x^3*(1 + x)^4).

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1,4,6,4,1).

%F a(n) = a(n-3) + 4*a(n-4) + 6*a(n-5) + 4*a(n-6) + a(n-7).

%F a(n) = Sum_{k=0..floor(n/3)} binomial(4*k+1,n-3*k).

%F a(n) = A375318(n) + A375318(n-1).

%o (PARI) my(N=40, x='x+O('x^N)); Vec((1+x)/(1-x^3*(1+x)^4))

%o (PARI) a(n) = sum(k=0, n\3, binomial(4*k+1, n-3*k));

%Y Cf. A375316, A375318.

%K nonn

%O 0,5

%A _Seiichi Manyama_, Aug 12 2024