A191798 Number of essentially different ways of arranging numbers 1 through 2*n around a circle so that the sums of each pair of adjacent numbers are neither all prime nor all composite.

0, 2, 58, 2474, 180480, 19895936, 3105348340, 652948189204, 177662757810868, 60772232945639507, 25533219938917963508, 12921764841857675170314, 7754002391777621430686566

Offset

1,2

Comments

Finding a pattern, recurrence relation or explicit formula for this sequence would allow us to find terms in A191374 using terms from A051252, or vice versa.

Links

Table of n, a(n) for n=1..13.

Formula

For n>1, a(n) = (2*n-1)!/2 - A051252(n) - A191374(n).

Example

a(2) = 2 since the arrangements 1,3,2,4 and 1,3,4,2 both satisfy the condition.

Crossrefs

Cf. A051252, A191374.

Sequence in context: A285148 A115610 A341082 * A206531 A290306 A113635

Adjacent sequences: A191795 A191796 A191797 * A191799 A191800 A191801

Keyword

nonn,more

Author

Bennett Gardiner, Jun 16 2011

Extensions

a(7) corrected, a(8)-a(13) added by Max Alekseyev, Aug 19 2013

Status

approved