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 A151583 #15 Jul 15 2020 06:18:52 %S A151583 0,2,45,260,1115,4230,15113,52232,176823,590090,1948133,6376716, %T A151583 20725523,66960782,215232705,688746512,2195381615,6973567506, %U A151583 22082966429,69735686420,219667415499,690383309462,2165293110905,6778308873240,21182215233575,66088511533850 %N A151583 Number of permutations of 2 indistinguishable copies of 1..n arranged in a circle with exactly 2 adjacent element pairs in decreasing order. %H A151583 Andrew Howroyd, <a href="/A151583/b151583.txt">Table of n, a(n) for n = 1..500</a> %H A151583 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (9,-30,46,-33,9). %F A151583 a(n) = n*(3^n - 4*n) for n > 1. - _Andrew Howroyd_, May 04 2020 %F A151583 From _Colin Barker_, Jul 15 2020: (Start) %F A151583 G.f.: x^2*(2 + 27*x - 85*x^2 + 33*x^3 - 9*x^4) / ((1 - x)^3*(1 - 3*x)^2). %F A151583 a(n) = 9*a(n-1) - 30*a(n-2) + 46*a(n-3) - 33*a(n-4) + 9*a(n-5) for n>6. %F A151583 (End) %o A151583 (PARI) a(n) = if(n <= 1, 0, n*(3^n - 4*n)) \\ _Andrew Howroyd_, May 04 2020 %o A151583 (PARI) concat(0, Vec(x^2*(2 + 27*x - 85*x^2 + 33*x^3 - 9*x^4) / ((1 - x)^3*(1 - 3*x)^2) + O(x^30))) \\ _Colin Barker_, Jul 15 2020 %Y A151583 With 3..8 descents: A151584, A151585, A151586, A151587, A151588, A151589. %Y A151583 With 3..7 copies of 1..n: A151590, A151597, A151603, A151607, A151610. %Y A151583 Cf. A151576, A151624. %K A151583 nonn,easy %O A151583 1,2 %A A151583 _R. H. Hardin_, May 21 2009 %E A151583 Terms a(13) and beyond from _Andrew Howroyd_, May 04 2020