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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 13 13:40 EDT 2021. Contains 344999 sequences. (Running on oeis4.)