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A287583 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 four. 2
1, 1, 2, 5, 15, 52, 187, 677, 2439, 8707, 30871, 108696, 380653, 1328193, 4623194, 16065161, 55763738, 193430602, 670683122, 2324853720, 8057594663, 27923827498, 96765523944, 335314355594, 1161917842116, 4026187435945, 13951144657754, 48341945365173 (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 (5,-4,-1,-7,-46,76,53,113,-164,-256,-103,182,370,9,-105,-198,31,42,40,-21,-20,-3,4,4)

FORMULA

G.f.: -(4*x^23 +8*x^22 +21*x^21 +5*x^20 -16*x^19 +24*x^18 +76*x^17 +176*x^16 +25*x^15 -80*x^14 -119*x^13 +169*x^12 +324*x^11 +259*x^10 +26*x^9 -129*x^8 -37*x^7 -24*x^6 +52*x^5 +6*x^4 +x^2 -4*x +1) / ((4*x^16 +4*x^15 -3*x^14 -4*x^13 -13*x^12 +20*x^11 +16*x^10 -13*x^9 -68*x^8 -81*x^7 -36*x^6 -4*x^5 +23*x^4 +11*x^3 +4*x^2 +x -1)*(x -1)^2*(x^3 +x^2 +x -1)^2).

a(n) = A000110(n) for n <= 5.

CROSSREFS

Column k=4 of A287417.

Cf. A000110.

Sequence in context: A192553 A053553 A276721 * A287276 A007312 A007296

Adjacent sequences:  A287580 A287581 A287582 * A287584 A287585 A287586

KEYWORD

nonn,easy

AUTHOR

Alois P. Heinz, May 26 2017

STATUS

approved

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Last modified June 19 12:33 EDT 2021. Contains 345128 sequences. (Running on oeis4.)