A392545 - OEIS

%I #14 Jan 16 2026 09:14:59

%S 1,4,10,20,35,56,84,121,173,256,406,694,1247,2276,4113,7263,12487,

%T 20952,34519,56296,91667,150129,248442,415853,702561,1193284,2029036,

%U 3442498,5816480,9782234,16386865,27380039,45704706,76332852,127678961,213973997

%N Expansion of 1 / ((1-x)^4 - x^7).

%H Seiichi Manyama, <a href="/A392545/b392545.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 (4,-6,4,-1,0,0,1).

%F a(n) = Sum_{k=0..floor(n/7)} binomial(n-3*k+3,n-7*k).

%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) + a(n-7).

%o (PARI) my(N=40, x='x+O('x^N)); Vec(1/((1-x)^4-x^7))

%Y Cf. A005709, A049017, A392543, A392544, A392546, A392547.

%K nonn,easy

%O 0,2

%A _Seiichi Manyama_, Jan 15 2026