A321049 Number of permutations of [n] with no fixed points where the maximal displacement of an element equals three.

0, 5, 18, 44, 116, 331, 932, 2532, 6720, 17804, 47280, 125460, 331736, 874973, 2305750, 6075184, 16001968, 42130767, 110885496, 291792264, 767776064, 2020061968, 5314529928, 13981117152, 36779372688, 96751538581, 254510051546, 669494097852, 1761102380100

Offset: 3

Author

Alois P. Heinz, Oct 26 2018

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 3..1000
• Index entries for linear recurrences with constant coefficients, signature (3,0,-3,6,-7,-11,-14,0,16,18,6,-7,1,-2,1,-2,-1,1).

Crossrefs

Column k=3 of A259784.

Cf. A033305, A079997.

Formula

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

a(n) = A079997(n) - A033305(n).