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 A384328 #40 Jun 09 2025 21:10:28
%S A384328 1,3,6,10,15,21,28,37,48,61,76,93,112,133,157,184,214,247,283,322,364,
%T A384328 410,460,514,572,634,700,770,845,925,1010,1100,1195,1295,1400,1511,
%U A384328 1628,1751,1880,2015,2156,2303,2457,2618,2786,2961
%N A384328 Expansion of 1 / ((1-x)^3 * (1-x^7)).
%C A384328 Number of nonnegative integer solutions of equation x + y + z + 7*w=n.
%C A384328 a(n) is the number of partitions of n into parts 1 of three kinds and 7 (of one kind). - _Joerg Arndt_, May 28 2025
%H A384328 Hoang Xuan Thanh, <a href="/A384328/b384328.txt">Table of n, a(n) for n = 0..1999</a>
%H A384328 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1,0,0,0,1,-3,3,-1).
%F A384328 a(n) = ((n+2) * (n+9) * (n+4) - (r+2) * (r-5) * (r-3)) / 42 where r = n mod 7.
%F A384328 a(n) = floor((n+3) * (n^2+12*n+26) / 42).
%o A384328 (PARI) my(x='x+O('x^50)); Vec(1/((1-x)^3*(1-x^7))) \\ _Michel Marcus_, May 27 2025
%Y A384328 Cf. A000292, A002623, A014125, A122046, A122047, A175724.
%K A384328 nonn,easy
%O A384328 0,2
%A A384328 _Hoang Xuan Thanh_, May 26 2025