cp's OEIS Frontend

A253171 a(n) = number of permutations of (1,2,...,n) producible by an ordered triple of distinct transpositions.

%I A253171 #11 Jun 13 2015 00:55:20
%S A253171 3,12,60,240,756,1988,4572,9495,18205,32736,55848,91182,143430,218520,
%T A253171 323816,468333,662967,920740,1257060,1689996,2240568,2933052,3795300,
%U A253171 4859075,6160401,7739928,9643312,11921610,14631690,17836656,21606288,26017497,31154795
%N A253171 a(n) = number of permutations of (1,2,...,n) producible by an ordered triple of distinct transpositions.
%H A253171 Colin Barker, <a href="/A253171/b253171.txt">Table of n, a(n) for n = 3..1000</a>
%H A253171 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F A253171 a(n) = n * (n^5 - 7*n^4 + 17*n^3 - 17*n^2 + 30*n - 24) / 48 for n>=3.
%F A253171 a(n) = C(n,2)*(C(n-2,2)*C(n-4,2)/6 + 1) + 2*C(n,3)*C(n-3,2) + 6*C(n,4) for n>=3.
%F A253171 G.f.: -x^3*(x^6-7*x^5+21*x^4-33*x^3+39*x^2-9*x+3) / (x-1)^7. - _Colin Barker_, Dec 30 2014
%e A253171 For n=4, the 12 permutations are 0132, 0213, 0321, 1023, 1230, 1302, 2031, 2103, 2310, 3012, 3120, and 3201. For example, 0123 is permuted into 0132 by ((b,d),(c,d), (b,c)).
%o A253171 (PARI) Vec(-x^3*(x^6-7*x^5+21*x^4-33*x^3+39*x^2-9*x+3)/(x-1)^7 + O(x^100)) \\ _Colin Barker_, Dec 30 2014
%Y A253171 Cf. A000914, for two transpositions.
%K A253171 nonn,easy
%O A253171 3,1
%A A253171 _Andrew Woods_, Dec 28 2014
%E A253171 More terms from _Colin Barker_, Dec 30 2014