A287275 - OEIS

A287275

Number of set partitions of [n] such that for each block all absolute differences between consecutive elements are <= three.

1, 1, 2, 5, 15, 47, 150, 481, 1545, 4965, 15958, 51293, 164871, 529947, 1703418, 5475329, 17599457, 56570281, 181834970, 584475733, 1878691887, 6038716423, 19410365422, 62391120801, 200545011401, 644615789581, 2072001259342, 6660074556205, 21407609138375

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OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Pierpaolo Natalini, Paolo Emilio Ricci, New Bell-Sheffer Polynomial Sets, Axioms 2018, 7(4), 71.

Wikipedia, Partition of a set

Index entries for linear recurrences with constant coefficients, signature (4,-2,-2,1).

FORMULA

G.f.: -(x^3-3*x+1)/((x-1)*(x^3-x^2-3*x+1)).

a(n) = A287214(n,3).

a(n) = A000110(n) for n <= 4.