A375362 - OEIS

%I #12 Aug 13 2024 11:38:19

%S 1,0,4,6,20,49,132,344,908,2384,6273,16492,43372,114050,299916,788673,

%T 2073944,5453760,14341528,37713312,99173121,260791400,685792228,

%U 1803399102,4742323108,12470688497,32793647356,86236081272,226771411940,596331286320

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

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,4,6,4,1).

%F a(n) = 4*a(n-2) + 6*a(n-3) + 4*a(n-4) + a(n-5).

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

%F a(n) = A375363(n) + A375363(n-1).

%o (PARI) my(N=30, x='x+O('x^N)); Vec(1/((1+x)*(1-x*(1+x)^3)))

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

%Y Cf. A375363.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 13 2024