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 A287992 #30 Feb 16 2025 08:33:47
%S A287992 1,26,129,444,1285,3366,8281,19544,44829,100770,223201,488916,1061749,
%T A287992 2289854,4910505,10480176,22275661,47178234,99605809,209704940,
%U A287992 440390181,922733526,1929364729,4026514824,8388588925,17448283346,36238762881,75161901444,155692535509,322122515310
%N A287992 Number of (undirected) paths in the prism graph Y_n.
%C A287992 Extended to a(1)-a(2) using the formula.
%H A287992 Colin Barker, <a href="/A287992/b287992.txt">Table of n, a(n) for n = 1..1000</a>
%H A287992 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphPath.html">Graph Path</a>.
%H A287992 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrismGraph.html">Prism Graph</a>.
%H A287992 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (8,-26,44,-41,20,-4).
%F A287992 a(n) = (5*2^(n + 1) - 5*n - n^2 - 13)*n.
%F A287992 From _Colin Barker_, Jun 04 2017: (Start)
%F A287992 G.f.: x*(1 + 18*x - 53*x^2 + 44*x^3 - 16*x^4) / ((1 - x)^4*(1 - 2*x)^2).
%F A287992 a(n) = 8*a(n-1) - 26*a(n-2) + 44*a(n-3) - 41*a(n-4) + 20*a(n-5) - 4*a(n-6) for n>6. (End)
%t A287992 Table[(5 2^(n + 1) - 5 n - n^2 - 13) n, {n, 20}]
%t A287992 LinearRecurrence[{8, -26, 44, -41, 20, -4}, {1, 26, 129, 444, 1285, 3366}, 20]
%t A287992 CoefficientList[Series[(1 + 18 x - 53 x^2 + 44 x^3 - 16 x^4)/((1 - x)^4 (1 - 2 x)^2), {x, 0, 20}], x]
%o A287992 (PARI) Vec(x*(1 + 18*x - 53*x^2 + 44*x^3 - 16*x^4) / ((1 - x)^4*(1 - 2*x)^2) + O(x^30)) \\ _Colin Barker_, Jun 04 2017
%Y A287992 Cf. A077265, A124350, A124349, A287988, A020874, A288516.
%K A287992 nonn,easy
%O A287992 1,2
%A A287992 _Eric W. Weisstein_, Jun 04 2017