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 A289792 #8 Feb 16 2025 08:33:49
%S A289792 0,0,0,0,90,540,1995,5775,14280,31500,63630,119790,212850,360360,
%T A289792 585585,918645,1397760,2070600,2995740,4244220,5901210,8067780,
%U A289792 10862775,14424795,18914280,24515700,31439850,39926250,50245650,62702640,77638365,95433345,116510400
%N A289792 Number of 4-cycles in the n-tetrahedral graph.
%C A289792 Extended to a(1)-a(5) using the formula.
%H A289792 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphCycle.html">Graph Cycle</a>
%H A289792 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TetrahedralGraph.html">Tetrahedral Graph</a>
%H A289792 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7, -21, 35, -35, 21, -7, 1).
%F A289792 a(n) = binomial(n - 1, 4) * (210 - 41*n + 7*n^2)/2.
%F A289792 a(n) = 7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)-7*a(n-6)+a(n-7).
%F A289792 G.f.: (-15*x^5*(6 - 6*x + 7*x^2))/(-1 + x)^7.
%t A289792 Table[Binomial[n - 1, 4] (210 - 41 n + 7 n^2)/2, {n, 20}]
%t A289792 LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 0, 0, 0, 90, 540, 1995}, 20]
%t A289792 CoefficientList[Series[-((15 x^4 (6 - 6 x + 7 x^2))/(-1 + x)^7), {x, 0, 20}], x]
%Y A289792 Cf. A027789 (3-cycles), A289793 (5-cycles), A289794 (6-cycles).
%K A289792 nonn,easy
%O A289792 1,5
%A A289792 _Eric W. Weisstein_, Jul 12 2017