A287582 Number of set partitions of [n] such that all absolute differences between least elements of consecutive blocks and between consecutive elements within the blocks are not larger than three.

1, 1, 2, 5, 15, 46, 139, 410, 1189, 3397, 9615, 27056, 75838, 212088, 592314, 1652806, 4609789, 12853354, 35832568, 99884249, 278414160, 776016655, 2162929636, 6028494326, 16802444328, 46831107603, 130525521011, 363794294041, 1013948759937, 2826024652739

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Wikipedia, Partition of a set

Index entries for linear recurrences with constant coefficients, signature (4,-2,-2,-10,11,10,-6,-7,1,2)

Formula

G.f.: -(2*x^9+7*x^8-6*x^6-x^5+11*x^4+x^3-3*x+1) / ((x^2+x-1) * (2*x^6 +3*x^5 -6*x^3 -3*x^2 -x+1) * (x-1)^2).

a(n) = A000110(n) for n <= 4.

Crossrefs

Column k=3 of A287417.

Cf. A000110.

Sequence in context: A149913 A065848 A148359 * A122392 A139782 A047086

Adjacent sequences: A287579 A287580 A287581 * A287583 A287584 A287585

Keyword

nonn,easy

Author

Alois P. Heinz, May 26 2017

Status

approved