A392552 - OEIS

%I #12 Jan 16 2026 09:14:27

%S 1,4,10,20,37,68,126,232,420,748,1318,2308,4023,6980,12054,20728,

%T 35515,60664,103340,175600,297704,503656,850460,1433560,2412573,

%U 4054148,6803298,11402028,19086465,31914204,53307530,88954328,148301324,247027700,411140514,683751740

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

%H Seiichi Manyama, <a href="/A392552/b392552.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,1,-4,2,0,-1).

%F a(n) = Sum_{k=0..floor(n/4)} (k+1) * binomial(n-2*k+3,n-4*k).

%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) + a(n-4) - 4*a(n-5) + 2*a(n-6) - a(n-8).

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

%Y Cf. A024490, A292324.

%K nonn,easy

%O 0,2

%A _Seiichi Manyama_, Jan 16 2026