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

4,1

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)

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).

Mathematica

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

Crossrefs

Column k=3 of A287213.

Cf. A001519, A287275.

Sequence in context: A290721 A354942 A205532 * A353177 A089130 A081340

Adjacent sequences: A294049 A294050 A294051 * A294053 A294054 A294055

Keyword

nonn,easy

Author

Alois P. Heinz, Oct 22 2017

Status

approved