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 A384562 #13 Aug 04 2025 11:21:05
%S A384562 0,0,0,0,0,0,0,0,0,0,1,5,12,24,42,66,98,135,181,233,298,367,452,543,
%T A384562 651,765,899,1039,1202,1371,1564,1765,1993,2227,2491,2763,3066,3377,
%U A384562 3722,4075,4465,4863,5299,5745,6232,6727,7266,7815,8409,9013,9665,10327,11040,11763,12538,13325,14167,15019,15929,16851,17832,18825,19880,20947,22079,23223,24433,25657,26950
%N A384562 Number of integer partitions of n with origin-to-boundary graph-distance equal to 4.
%C A384562 This also counts the number of partitions of n with a fixed Durfee triangle of size 4. This is the column k=4 of the triangle in A325188.
%H A384562 Michael De Vlieger, <a href="/A384562/b384562.txt">Table of n, a(n) for n = 0..10000</a>
%H A384562 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. 13.
%H A384562 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,0,0,-2,0,0,1,1,-1).
%F A384562 G.f.: q^10*(1 + 4*q + 6*q^2 + 7*q^3 + 6*q^4 + 2*q^5 - 5*q^7 - 5*q^8 - 5*q^9 + q^11 + 3*q^12 + 2*q^13 - q^16)/((1 - q)*(1 - q^2)*(1 - q^3)*(1 - q^4)).
%t A384562 CoefficientList[Series[(q^10 (1 + 4q + 6 q^2 + 7 q^3 + 6 q^4 + 2 q^5 - 5 q^7 - 5 q^8 - 5 q^9 + q^11 + 3 q^12 + 2 q^13 - q^16))/((1 - q)(1 - q^2)(1 - q^3)(1 - q^4)), {q, 0, 50}], q]
%Y A384562 Cf. A130130, A325168, A325188, A382682.
%K A384562 nonn,easy
%O A384562 0,12
%A A384562 _N Guru Sharan_, Jun 03 2025