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A287275 Number of set partitions of [n] such that for each block all absolute differences between consecutive elements are <= three.

%I A287275 #10 Dec 27 2018 20:47:35
%S A287275 1,1,2,5,15,47,150,481,1545,4965,15958,51293,164871,529947,1703418,
%T A287275 5475329,17599457,56570281,181834970,584475733,1878691887,6038716423,
%U A287275 19410365422,62391120801,200545011401,644615789581,2072001259342,6660074556205,21407609138375
%N A287275 Number of set partitions of [n] such that for each block all absolute differences between consecutive elements are <= three.
%H A287275 Alois P. Heinz, <a href="/A287275/b287275.txt">Table of n, a(n) for n = 0..1000</a>
%H A287275 Pierpaolo Natalini, Paolo Emilio Ricci, <a href="https://doi.org/10.3390/axioms7040071">New Bell-Sheffer Polynomial Sets</a>, Axioms 2018, 7(4), 71.
%H A287275 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%H A287275 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-2,-2,1).
%F A287275 G.f.: -(x^3-3*x+1)/((x-1)*(x^3-x^2-3*x+1)).
%F A287275 a(n) = A287214(n,3).
%F A287275 a(n) = A000110(n) for n <= 4.
%e A287275 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.
%Y A287275 Column k=3 of A287214.
%Y A287275 Cf. A000110.
%K A287275 nonn,easy
%O A287275 0,3
%A A287275 _Alois P. Heinz_, May 22 2017