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A253171 a(n) = number of permutations of (1,2,...,n) producible by an ordered triple of distinct transpositions. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 7 11:34 EDT 2020. Contains 336275 sequences. (Running on oeis4.)