A392490 - OEIS

%I #14 Jan 14 2026 10:35:29

%S 1,0,0,2,0,0,3,1,0,4,4,0,5,10,1,6,20,6,7,35,21,9,56,56,17,84,126,46,

%T 121,252,131,175,462,342,275,793,805,506,1299,1730,1079,2080,3448,

%U 2457,3367,6465,5565,5733,11562,12121,10556,20026,25142,20944,34223,49725

%N a(n) = Sum_{k=0..floor(n/3)} binomial(k+1,2*n-6*k+1).

%H Seiichi Manyama, <a href="/A392490/b392490.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,2,0,0,-1,1).

%F G.f.: 1 / ((1-x^3)^2 - x^7).

%F a(n) = 2*a(n-3) - a(n-6) + a(n-7).

%o (PARI) my(N=60, x='x+O('x^N)); Vec(1/((1-x^3)^2-x^7))

%Y Cf. A005314, A392489, A392491.

%Y Cf. A390020, A390662.

%K nonn,easy

%O 0,4

%A _Seiichi Manyama_, Jan 14 2026