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 A289793 #8 Feb 16 2025 08:33:49
%S A289793 0,0,0,0,312,3024,14868,51744,145152,350784,759528,1511136,2810808,
%T A289793 4948944,8324316,13470912,21088704,32078592,47581776,69023808,
%U A289793 98163576,137147472,188568996,255534048,341732160,451513920,589974840,763045920,977591160,1241512272
%N A289793 Number of 5-cycles in the n-tetrahedral graph.
%C A289793 Extended to a(1)-a(5) using the formula.
%H A289793 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphCycle.html">Graph Cycle</a>
%H A289793 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TetrahedralGraph.html">Tetrahedral Graph</a>
%H A289793 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8, -28, 56, -70, 56, -28, 8, -1).
%F A289793 a(n) = 6*binomial(n, 5)*(-78 + 21*n + n^2).
%F A289793 a(n) = 8*a(n-1)-28*a(n-2)+56*a(n-3)-70*a(n-4)+56*a(n-5)-28*a(n-6)+8*a(n-7)-a(n-8).
%F A289793 G.f.: (-12*x^5*(-26 - 44*x + 49*x^2))/(-1 + x)^8.
%t A289793 Table[6 Binomial[n, 5] (-78 + 21 n + n^2), {n, 20}]
%t A289793 LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {0, 0, 0, 0, 312, 3024, 14868, 51744}, 20]
%t A289793 CoefficientList[Series[-((12 x^4 (-26 - 44 x + 49 x^2))/(-1 + x)^8), {x, 0, 20}], x]
%Y A289793 Cf. A027789 (3-cycles), A289792 (4-cycles), A289794 (6-cycles).
%K A289793 nonn,easy
%O A289793 1,5
%A A289793 _Eric W. Weisstein_, Jul 12 2017