A392488 - OEIS

%I #9 Jan 14 2026 10:36:52

%S 1,0,0,1,3,0,0,5,10,1,1,21,35,7,9,84,126,37,56,330,462,178,297,1287,

%T 1717,820,1443,5006,6452,3683,6643,19464,24481,16252,29512,75739,

%U 93709,70737,127909,295152,361590,304437,544603,1152351,1405418,1297892,2288483

%N a(n) = Sum_{k=0..floor((2*n+1)/7)} binomial(2*k+1,2*n-7*k+1).

%H Seiichi Manyama, <a href="/A392488/b392488.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,4,0,0,1,-2,1).

%F G.f.: (1 + x^3 - x^4) / (1 - 4*x^4 - x^7*(1-x)^2).

%F a(n) = 4*a(n-4) + a(n-7) - 2*a(n-8) + a(n-9).

%o (PARI) my(N=50, x='x+O('x^N)); Vec((1+x^3-x^4)/(1-4*x^4-x^7*(1-x)^2))

%Y Cf. A392456.

%K nonn,easy

%O 0,5

%A _Seiichi Manyama_, Jan 14 2026