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 A151590 #13 Jul 16 2020 13:32:22 %S A151590 0,12,207,1392,7455,36540,171591,785856,3538215,15727740,69204927, %T A151590 301988592,1308621327,5637142812,24159189015,103079212800, %U A151590 438086661591,1855425868956,7834020344655,32985348829680,138538465095807,580542139461372,2427721674124647 %N A151590 Number of permutations of 3 indistinguishable copies of 1..n arranged in a circle with exactly 2 adjacent element pairs in decreasing order. %H A151590 Andrew Howroyd, <a href="/A151590/b151590.txt">Table of n, a(n) for n = 1..500</a> %H A151590 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (11,-43,73,-56,16). %F A151590 a(n) = n*((3/2)*4^n - 9*n) for n > 1. - _Andrew Howroyd_, May 04 2020 %F A151590 From _Colin Barker_, Jul 16 2020: (Start) %F A151590 G.f.: 3*x^2*(4 + 25*x - 123*x^2 + 56*x^3 - 16*x^4) / ((1 - x)^3*(1 - 4*x)^2). %F A151590 a(n) = 11*a(n-1) - 43*a(n-2) + 73*a(n-3) - 56*a(n-4) + 16*a(n-5) for n>6. %F A151590 (End) %o A151590 (PARI) a(n) = if(n <= 1, 0, n*(3*4^n/2 - 9*n)) \\ _Andrew Howroyd_, May 04 2020 %o A151590 (PARI) concat(0, Vec(3*x^2*(4 + 25*x - 123*x^2 + 56*x^3 - 16*x^4) / ((1 - x)^3*(1 - 4*x)^2) + O(x^40))) \\ _Colin Barker_, Jul 16 2020 %Y A151590 Cf. A151583. %K A151590 nonn,easy %O A151590 1,2 %A A151590 _R. H. Hardin_, May 21 2009 %E A151590 Terms a(9) and beyond from _Andrew Howroyd_, May 04 2020