%I #11 Nov 22 2023 14:55:34

%S 2,13,61,248,935,3368,11777,40347,136214,454922,1507000,4961100,

%T 16253188,53045703,172607505,560317916,1815445901,5873136282,

%U 18976870985,61256217631,197573796328,636837047532,2051636248268,6606758265032,21268025275930,68445465415825

%N Number of set partitions of [n] such that the maximal absolute difference between consecutive elements within a block equals three.

%H Alois P. Heinz, <a href="/A294052/b294052.txt">Table of n, a(n) for n = 4..1000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (7,-15,8,5,-5,1)

%F G.f.: (x-2)*x^4/((x-1)*(x^2-3*x+1)*(x^3-x^2-3*x+1)).

%F a(n) = A287275(n) - A001519(n).

%t LinearRecurrence[{7,-15,8,5,-5,1},{2,13,61,248,935,3368},30] (* _Harvey P. Dale_, Nov 22 2023 *)

%Y Column k=3 of A287213.

%Y Cf. A001519, A287275.

%K nonn,easy

%O 4,1

%A _Alois P. Heinz_, Oct 22 2017