A294053 Number of set partitions of [n] such that the maximal absolute difference between consecutive elements within a block equals four.

5, 38, 215, 1061, 4835, 20973, 88010, 360787, 1453978, 5784863, 22790024, 89092968, 346161413, 1338360327, 5153828402, 19781784669, 75723483993, 289218958150, 1102597884045, 4196961350447, 15954736073286, 60585891849501, 229855881578197, 871373727460242

Offset: 5

Author

Alois P. Heinz, Oct 22 2017

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 5..1000
• Index entries for linear recurrences with constant coefficients, signature (9,-26,23,0,20,-40,2,16,-1,0,-3,1)

Crossrefs

Column k=4 of A287213.

Cf. A287275, A287276.

Programs

Mathematica

Drop[CoefficientList[Series[(x^5-2x^4+x^3-3x^2+7x-5)x^5/((x-1)(x^3-x^2- 3x+1)(x^8-x^7-7x^5+7x^4+x^3+4x^2-5x+1)),{x,0,30}],x],5] (* or *) LinearRecurrence[{9,-26,23,0,20,-40,2,16,-1,0,-3,1},{5,38,215,1061,4835,20973,88010,360787,1453978,5784863,22790024,89092968},30] (* Harvey P. Dale, May 25 2022 *)

Formula

G.f.: (x^5-2*x^4+x^3-3*x^2+7*x-5)*x^5 / ((x-1) *(x^3-x^2-3*x+1) *(x^8 -x^7 -7*x^5 +7*x^4 +x^3 +4*x^2 -5*x+1)).

a(n) = A287276(n) - A287275(n).