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

5,1

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)

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).

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 *)

Crossrefs

Column k=4 of A287213.

Cf. A287275, A287276.

Sequence in context: A145156 A318102 A163698 * A345686 A279265 A129048

Adjacent sequences: A294050 A294051 A294052 * A294054 A294055 A294056

Keyword

nonn,easy

Author

Alois P. Heinz, Oct 22 2017

Status

approved