A323799 Number of permutations p of [n] such that max_{j=1..n} |p(j)-j| = 3.

0, 10, 47, 157, 503, 1669, 5472, 17531, 55135, 172134, 535510, 1660795, 5133470, 15826173, 48706210, 149721544, 459820058, 1411142937, 4328181110, 13269541967, 40669595890, 124617708274, 381776661185, 1169438884559, 3581781480980, 10969462410857, 33592685042253

Offset: 3

Author

Alois P. Heinz, Jan 28 2019

Keywords

• nonn
• easy

Examples

			a(4) = 10: 2341, 2431, 3241, 3421, 4123, 4132, 4213, 4231, 4312, 4321.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 3..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-2,-2,6,-17,-16,-30,6,32,48,12,-16,-16,-9,2,-2,-2,2,1).

Crossrefs

Column k=3 of A130152.

Cf. A002524, A002526.

Formula

G.f.: x^4 *(x^11+x^10-3*x^9+x^8+4*x^7-4*x^6-4*x^5-5*x^4+11*x^3+11*x^2-7*x-10) / ((x-1) *(x^5 -2*x^3 -2*x+1) *(x^13 +3*x^12 +3*x^11 +5*x^10 +9*x^9 +7*x^8 -3*x^7 -19*x^6 -21*x^5 -13*x^4 -3*x^3 -3*x^2-x+1)).

a(n) = A002526(n) - A002524(n).