A294052 Number of set partitions of [n] such that the maximal absolute difference between consecutive elements within a block equals three.

2, 13, 61, 248, 935, 3368, 11777, 40347, 136214, 454922, 1507000, 4961100, 16253188, 53045703, 172607505, 560317916, 1815445901, 5873136282, 18976870985, 61256217631, 197573796328, 636837047532, 2051636248268, 6606758265032, 21268025275930, 68445465415825

Offset: 4

Author

Alois P. Heinz, Oct 22 2017

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 4..1000
• Index entries for linear recurrences with constant coefficients, signature (7,-15,8,5,-5,1)

Crossrefs

Column k=3 of A287213.

Cf. A001519, A287275.

Programs

Mathematica

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

Formula

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

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