A390688 - OEIS

%I #23 Jan 12 2026 08:46:55

%S 1,0,0,0,0,2,0,0,0,1,3,0,0,0,4,4,0,0,1,10,5,0,0,6,20,6,0,1,21,35,7,0,

%T 8,56,56,8,1,36,126,84,9,10,120,252,120,11,55,330,462,165,23,220,792,

%U 792,221,90,715,1716,1287,300,377,2002,3432,2003,469,1379,5005,6435

%N a(n) = Sum_{k=0..floor(2*n/9)} binomial(k+1,2*n-9*k).

%H Seiichi Manyama, <a href="/A390688/b390688.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,2,0,0,0,1,-1).

%F G.f.: 1 / ((1-x^5)^2 - x^9).

%F a(n) = 2*a(n-5) + a(n-9) - a(n-10).

%o (PARI) my(N=70, x='x+O('x^N)); Vec(1/((1-x^5)^2-x^9))

%Y Cf. A001906, A005251, A122514, A392250, A390020, A391399, A390662.

%K nonn,easy

%O 0,6

%A _Seiichi Manyama_, Jan 12 2026