%I #13 Sep 30 2023 12:21:02
%S 1,1,1,1,1,1,2,3,3,3,3,3,4,5,6,6,6,6,7,8,9,10,10,10,11,12,13,14,15,15,
%T 16,17,18,19,20,21,22,23,24,25,26,27,29,30,31,32,33,34,36,38,39,40,41,
%U 42,44,46,48,49,50,51,53
%N Expansion of 1/((1-x)*(1-x^6)*(1-x^7)).
%C Number of partitions of n into parts 1, 6, and 7. - _Joerg Arndt_, Oct 12 2014
%H <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, -1, 1).
%t CoefficientList[Series[1/((1-x)(1-x^6)(1-x^7)),{x,0,60}],x] (* or *) LinearRecurrence[{1,0,0,0,0,1,0,-1,0,0,0,0,-1,1},{1,1,1,1,1,1,2,3,3,3,3,3,4,5},70] (* _Harvey P. Dale_, Dec 30 2021 *)
%o (PARI) a(n)=round((n^2+14*n+18)/84+369830\7^(n%7)%7/7) \\ _Tani Akinari_, Oct 13 2014
%K nonn
%O 0,7
%A _N. J. A. Sloane_.