

A287275


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


4



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 BellSheffer 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^33*x+1)/((x1)*(x^3x^23*x+1)).
a(n) = A287214(n,3).
a(n) = A000110(n) for n <= 4.


EXAMPLE

a(5) = 47 = 52  5 = A000110(5)  5 counts all set partitions of [5] except: 15234, 15234, 15243, 15234, 15234.


CROSSREFS

Column k=3 of A287214.
Cf. A000110.
Sequence in context: A143094 A308274 A058495 * A151280 A149914 A071735
Adjacent sequences: A287272 A287273 A287274 * A287276 A287277 A287278


KEYWORD

nonn,easy


AUTHOR

Alois P. Heinz, May 22 2017


STATUS

approved



