A159277 Ways to write the identity as a product of n 3-cycles in symmetric group S_4.

1, 0, 8, 32, 384, 2560, 22528, 172032, 1409024, 11141120, 89653248, 715128832, 5729419264, 45801799680, 366548615168, 2931852050432, 23456963887104, 187647121162240, 1501211329036288, 12009553193336832, 96076975302508544

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Flavien Mabilat, Some counting formulas for λ-quiddities over the rings Z / 2^m Z, arXiv:2402.09968 [math.CO], 2024.

Formula

a(n+1) = (2/3)*(-1)^n*((-8)^n-4^n).

O.g.f.: 1 - 8*x^2/(32*x^2+4*x-1).

a(n) = 8 * A091904(n-1). - R. J. Mathar, Jun 28 2009

Crossrefs

Cf. A091904.

Sequence in context: A348399 A208824 A034193 * A214539 A140789 A120781

Adjacent sequences: A159274 A159275 A159276 * A159278 A159279 A159280

Keyword

easy,nonn

Author

Jacob A. Siehler, Apr 07 2009

Extensions

Offset corrected by R. J. Mathar, Jun 28 2009

Offset changed back and a(0) = 1 prepended by Andrey Zabolotskiy, Feb 21 2024

Status

approved