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

Offset: 0

Author

Alois P. Heinz, May 22 2017

Keywords

• nonn
• easy

Examples

			a(5) = 47 = 52 - 5 = A000110(5) - 5 counts all set partitions of [5] except: 15|234, 15|23|4, 15|24|3, 15|2|34, 15|2|3|4.
		

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).

Crossrefs

Column k=3 of A287214.

Cf. A000110.

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.