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

3, 12, 60, 240, 756, 1988, 4572, 9495, 18205, 32736, 55848, 91182, 143430, 218520, 323816, 468333, 662967, 920740, 1257060, 1689996, 2240568, 2933052, 3795300, 4859075, 6160401, 7739928, 9643312, 11921610, 14631690, 17836656, 21606288, 26017497, 31154795

Offset

3,1

Links

Colin Barker, Table of n, a(n) for n = 3..1000

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

a(n) = n * (n^5 - 7*n^4 + 17*n^3 - 17*n^2 + 30*n - 24) / 48 for n>=3.

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.

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

Example

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)).

Prog

(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

Crossrefs

Cf. A000914, for two transpositions.

Sequence in context: A233283 A127918 A069944 * A073996 A003483 A278395

Adjacent sequences: A253168 A253169 A253170 * A253172 A253173 A253174

Keyword

nonn,easy

Author

Andrew Woods, Dec 28 2014

Extensions

More terms from Colin Barker, Dec 30 2014

Status

approved