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 A382682 #48 Aug 05 2025 10:29:06
%S A382682 0,0,0,0,0,0,1,4,8,15,23,32,43,54,67,82,97,114,133,152,173,196,219,
%T A382682 244,271,298,327,358,389,422,457,492,529,568,607,648,691,734,779,826,
%U A382682 873,922,973,1024,1077,1132,1187,1244,1303,1362,1423,1486,1549,1614,1681,1748,1817,1888,1959
%N A382682 Number of integer partitions of n with origin-to-boundary graph-distance equal to 3.
%C A382682 Also the number of partitions of n with a fixed Durfee triangle of size 3.
%C A382682 Column k=3 of the triangle in A325188.
%H A382682 Michael De Vlieger, <a href="/A382682/b382682.txt">Table of n, a(n) for n = 0..10000</a>
%H A382682 N. Guru Sharan and Armin Straub, <a href="https://arxiv.org/abs/2507.19047">Partitions with Durfee triangles of fixed size</a>, arXiv:2507.19047 [math.CO], 2025. See p. 10.
%H A382682 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,1,-2,1).
%F A382682 G.f.: q^6*(1 + 2*q + q^2 + 2*q^3 - q^4 - q^6 - q^7 + q^8)/((1 - q)^3*(1 + q + q^2)).
%F A382682 9*a(n) = 2*A099837(n+3)+6*n^2+59-45*n for n>9. - _R. J. Mathar_, Jun 24 2025
%t A382682 CoefficientList[Series[(q^6 + 2 q^7 + q^8 + 2 q^9 - q^10 - q^12 - q^13 + q^14)/((1 - q)^3 (1 + q + q^2)), {q, 0, 200}],q]
%Y A382682 Cf. A130130, A325168, A325188.
%K A382682 nonn,easy
%O A382682 0,8
%A A382682 _N Guru Sharan_, Jun 03 2025