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 A297662 #14 Feb 16 2025 08:33:52
%S A297662 0,3,27,108,300,675,1323,2352,3888,6075,9075,13068,18252,24843,33075,
%T A297662 43200,55488,70227,87723,108300,132300,160083,192027,228528,270000,
%U A297662 316875,369603,428652,494508,567675,648675,738048,836352,944163,1062075,1190700
%N A297662 Number of chordless cycles in the complete tripartite graph K_{n,n,n}.
%C A297662 The only chordless cycles in a complete tripartite graph are cycles of length 4 confined to two of the partitions. - _Andrew Howroyd_, Jan 03 2018
%H A297662 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ChordlessCycle.html">Chordless Cycle</a>
%H A297662 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CompleteTripartiteGraph.html">Complete Tripartite Graph</a>
%H A297662 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5, -10, 10, -5, 1).
%F A297662 a(n) = 3*n^2*(n-1)^2/4 = 3*A000537(n). - _Andrew Howroyd_, Jan 03 2018
%F A297662 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
%F A297662 G.f.: -3*x^2*(1 + 4*x + x^2)/(-1 + x)^5.
%t A297662 Table[3 Binomial[n, 2]^2, {n, 20}]
%t A297662 3 Binomial[Range[20], 2]^2
%t A297662 LinearRecurrence[{5, -10, 10, -5, 1}, {0, 3, 27, 108, 300}, 20]
%t A297662 SeriesCoefficient[Series[-3 x (1 + 4 x + x^2)/(-1 + x)^5, {x, 0, 20}], x]
%o A297662 (PARI) a(n) = 3*n^2*(n-1)^2/4; \\ _Andrew Howroyd_, Jan 03 2018
%Y A297662 Cf. A000537, A234616.
%K A297662 nonn,easy
%O A297662 1,2
%A A297662 _Eric W. Weisstein_, Jan 02 2018
%E A297662 a(6)-a(36) from _Andrew Howroyd_, Jan 03 2018