A392543 - OEIS

%I #19 Jan 18 2026 14:16:07

%S 1,2,3,4,5,6,7,9,13,20,31,47,69,98,136,187,258,360,509,727,1043,1495,

%T 2134,3031,4288,6054,8547,12083,17114,24279,34475,48959,69497,98582,

%U 139750,198032,280593,397629,563624,799116,1133190,1607014,2278870,3231319,4581397

%N Expansion of 1 / ((1-x)^2 - x^7).

%H Seiichi Manyama, <a href="/A392543/b392543.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 (2,-1,0,0,0,0,1).

%F a(n) = Sum_{k=0..floor(n/7)} binomial(n-5*k+1,n-7*k).

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

%t CoefficientList[Series[1/((1-x)^2-x^7),{x,0,60}],x] (* _Vincenzo Librandi_, Jan 17 2026 *)

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

%o (Magma) m:=60; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R! 1 / ((1-x)^2 - x^7)); // _Vincenzo Librandi_, Jan 17 2026

%Y Cf. A005709, A049017, A392544, A392545, A392546, A392547.

%K nonn,easy

%O 0,2

%A _Seiichi Manyama_, Jan 15 2026