login
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

%I #12 Mar 30 2017 23:35:50

%S 0,2,58,2474,180480,19895936,3105348340,652948189204,177662757810868,

%T 60772232945639507,25533219938917963508,12921764841857675170314,

%U 7754002391777621430686566

%N 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.

%C 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.

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

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

%Y Cf. A051252, A191374.

%K nonn,more

%O 1,2

%A _Bennett Gardiner_, Jun 16 2011

%E a(7) corrected, a(8)-a(13) added by _Max Alekseyev_, Aug 19 2013