A375316 - OEIS

%I #10 Aug 12 2024 13:16:59

%S 1,1,1,5,11,19,42,98,205,429,936,2024,4316,9260,19949,42841,91917,

%T 197485,424331,911255,1957086,4203998,9029949,19394681,41657808,

%U 89478064,192189304,412801176,886657081,1904452689,4090567673,8786123349,18871714923,40534539675

%N Expansion of (1 + x)/(1 - x^2*(1 + x)^4).

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,4,6,4,1).

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

%F a(n) = Sum_{k=0..floor(n/2)} binomial(4*k+1,n-2*k).

%F a(n) = A375314(n) + A375314(n-1).

%o (PARI) my(N=40, x='x+O('x^N)); Vec((1+x)/(1-x^2*(1+x)^4))

%o (PARI) a(n) = sum(k=0, n\2, binomial(4*k+1, n-2*k));

%Y Cf. A093040, A375315.

%Y Cf. A375314.

%K nonn

%O 0,4

%A _Seiichi Manyama_, Aug 12 2024