This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A256322 #10 Aug 29 2024 16:07:07
%S A256322 0,4,16,37,65,102,147,200,261,331,408,494,588,690,800,919,1045,1180,
%T A256322 1323,1474,1633,1801,1976,2160,2352,2552,2760,2977,3201,3434,3675,
%U A256322 3924,4181,4447,4720,5002,5292,5590,5896,6211,6533,6864,7203,7550,7905,8269,8640
%N A256322 Number of partitions of 7n into exactly 3 parts.
%H A256322 Colin Barker, <a href="/A256322/b256322.txt">Table of n, a(n) for n = 0..1000</a>
%H A256322 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,0,-1,-1,1).
%F A256322 a(n) = a(n-1)+a(n-2)-a(n-4)-a(n-5)+a(n-6) for n>5.
%F A256322 G.f.: -x*(2*x^2+3*x+2)^2 / ((x-1)^3*(x+1)*(x^2+x+1)).
%e A256322 For n=1 the 4 partitions of 7*1 = 7 are [1, 1, 5], [1, 2, 4], [1, 3, 3] and [2, 2, 3].
%t A256322 Length /@ (Total /@ IntegerPartitions[7 #, {3}] & /@ Range[0, 46]) (* _Michael De Vlieger_, Mar 24 2015 *)
%t A256322 LinearRecurrence[{1,1,0,-1,-1,1},{0,4,16,37,65,102},50] (* _Harvey P. Dale_, Aug 29 2024 *)
%o A256322 (PARI) concat(0, vector(40, n, k=0; forpart(p=7*n, k++, , [3,3]); k))
%o A256322 (PARI) concat(0, Vec(-x*(2*x^2+3*x+2)^2/((x-1)^3*(x+1)*(x^2+x+1)) + O(x^100)))
%Y A256322 Cf. A033428 (6n), A256320 (4n), A256321 (5n).
%K A256322 nonn,easy
%O A256322 0,2
%A A256322 _Colin Barker_, Mar 24 2015