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A151624 Number of permutations of 2 indistinguishable copies of 1..n with exactly 2 adjacent element pairs in decreasing order. 5

%I

%S 0,1,48,603,5158,37257,247236,1568215,9703890,59226357,358722928,

%T 2163496611,13017647646,78225458401,469740168924,2819689366191,

%U 16922139539626,101545622110989,609314411814024,3656015481903355,21936500845191030,131620291694585721

%N Number of permutations of 2 indistinguishable copies of 1..n with exactly 2 adjacent element pairs in decreasing order.

%H Andrew Howroyd, <a href="/A151624/b151624.txt">Table of n, a(n) for n = 1..500</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (15,-84,226,-309,207,-54).

%F a(n) = 6^n - (2*n + 1)*3^n + n*(2*n + 1). - _Andrew Howroyd_, May 06 2020

%F From _Colin Barker_, Jul 16 2020: (Start)

%F G.f.: x^2*(1 + 33*x - 33*x^2 - 81*x^3) / ((1 - x)^3*(1 - 3*x)^2*(1 - 6*x)).

%F a(n) = 15*a(n-1) - 84*a(n-2) + 226*a(n-3) - 309*a(n-4) + 207*a(n-5) - 54*a(n-6) for n>6.

%F (End)

%o (PARI) a(n) = {6^n - (2*n + 1)*3^n + n*(2*n + 1)} \\ _Andrew Howroyd_, May 06 2020

%o (PARI) Vec(x^2*(1 + 33*x - 33*x^2 - 81*x^3) / ((1 - x)^3*(1 - 3*x)^2*(1 - 6*x)) + O(x^25)) \\ _Colin Barker_, Jul 16 2020

%Y Column k=2 of A154283.

%K nonn,easy

%O 1,3

%A _R. H. Hardin_, May 29 2009

%E Terms a(12) and beyond from _Andrew Howroyd_, May 06 2020

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Last modified May 12 13:02 EDT 2021. Contains 343823 sequences. (Running on oeis4.)