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

3,2

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).

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).

Crossrefs

Column k=3 of A259784.

Cf. A033305, A079997.

Sequence in context: A213397 A101105 A037140 * A007237 A327842 A000339

Adjacent sequences: A321046 A321047 A321048 * A321050 A321051 A321052

Keyword

nonn,easy

Author

Alois P. Heinz, Oct 26 2018

Status

approved