A389718 - OEIS

%I #20 Jan 09 2026 00:18:09

%S 1,0,0,1,0,0,1,0,0,1,0,0,1,0,1,1,0,6,1,0,21,1,0,56,1,0,126,1,1,252,1,

%T 11,462,1,66,792,1,286,1287,1,1001,2002,2,3003,3003,17,8008,4368,137,

%U 19448,6188,817,43758,8568,3877,92378,11629,15505,184756,15525,54265,352716,20580

%N a(n) = Sum_{k=0..floor(5*n/14)} binomial(k,5*n-14*k).

%H Seiichi Manyama, <a href="/A389718/b389718.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,5,0,0,-10,0,0,10,0,0,-5,0,1,1).

%F G.f.: (1-x^3)^4 / ((1-x^3)^5 - x^14).

%F a(n) = 5*a(n-3) - 10*a(n-6) + 10*a(n-9) - 5*a(n-12) + a(n-14) + a(n-15).

%o (PARI) my(N=70, x='x+O('x^N)); Vec((1-x^3)^4/((1-x^3)^5-x^14))

%Y Cf. A099131, A099132, A392356.

%Y Cf. A389717, A391265, A392272.

%K nonn,easy

%O 0,18

%A _Seiichi Manyama_, Jan 08 2026