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 A346637 #25 Mar 02 2024 12:27:11
%S A346637 0,1,32,243,1019,3095,7671,16527,32138,57789,97690,157091,242397,
%T A346637 361283,522809,737535,1017636,1377017,1831428,2398579,3098255,3952431,
%U A346637 4985387,6223823,7696974,9436725,11477726,13857507,16616593,19798619,23450445,27622271,32367752
%N A346637 a(n) is the number of quintuples (a_1,a_2,a_3,a_4,a_5) having all terms in {1,...,n} such that there exists a pentagon with these side-lengths.
%C A346637 The existence of such a five-sided polygon implies that every element of the quintuple is less than the sum of the other elements.
%H A346637 Giovanni Corbelli, <a href="/A346637/a346637.txt">Visual Basic routine for generating number of five-sided polygons</a>
%H A346637 Giovanni Corbelli <a href="https://bit.ly/ProofTuplesPolygons">Proof of the formula: Number of k-tuples with elements in {1,2,...,N} corresponding to k-sided polygons</a>
%H A346637 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A346637 a(n) = n^5 - 5*binomial(n+1,5) = n^5 - (n+1)*binomial(n,4).
%F A346637 General formula for k-tuples: a_k(n) = n^k - k*binomial(n+1,k) = n^k - (n+1)*binomial(n,k-1).
%F A346637 G.f.: x*(1 + 26*x + 66*x^2 + 21*x^3 + x^4)/(1 - x)^6. - _Stefano Spezia_, Sep 27 2021
%o A346637 (Visual Basic) ' See links.
%Y A346637 Cf. A006003, A346636, A346638.
%K A346637 nonn,easy
%O A346637 0,3
%A A346637 _Giovanni Corbelli_, Jul 26 2021