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

Author

Bennett Gardiner, Jun 16 2011

Keywords

• nonn
• more

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.

Examples

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

Crossrefs

Cf. A051252, A191374.

Formula

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

Extensions

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