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A287276 Number of set partitions of [n] such that for each block all absolute differences between consecutive elements are <= four.

%I A287276 #9 Jan 02 2021 16:41:29
%S A287276 1,1,2,5,15,52,188,696,2606,9800,36931,139303,525658,1983925,7488281,
%T A287276 28265353,106692425,402731694,1520195297,5738304135,21660476556,
%U A287276 81762200416,308629323572,1164989004846,4397506361848,16599351862867,62657893108843,236515956134402
%N A287276 Number of set partitions of [n] such that for each block all absolute differences between consecutive elements are <= four.
%H A287276 Alois P. Heinz, <a href="/A287276/b287276.txt">Table of n, a(n) for n = 0..1000</a>
%H A287276 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 A287276 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%H A287276 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (5,-4,-1,-7,7,0,1,-1).
%F A287276 G.f.: -(x^7+x^5-6*x^4-x^2+4*x-1)/(x^8-x^7-7*x^5+7*x^4+x^3+4*x^2-5*x+1).
%F A287276 a(n) = A287214(n,4).
%F A287276 a(n) = A000110(n) for n <= 5.
%e A287276 a(6) = 188 = 203 - 15 = A000110(6) - 15 counts all set partitions of [6] except: 16|2345, 16|234|5, 16|235|4, 16|23|45, 16|23|4|5, 16|245|3, 16|24|35, 16|24|3|5, 16|25|34, 16|2|345, 16|2|34|5, 16|25|3|4, 16|2|35|4, 16|2|3|45, 16|2|3|4|5.
%t A287276 LinearRecurrence[{5,-4,-1,-7,7,0,1,-1},{1,1,2,5,15,52,188,696},30] (* _Harvey P. Dale_, Jan 02 2021 *)
%Y A287276 Column k=4 of A287214.
%Y A287276 Cf. A000110.
%K A287276 nonn,easy
%O A287276 0,3
%A A287276 _Alois P. Heinz_, May 22 2017