A287584 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 five.

1, 1, 2, 5, 15, 52, 203, 824, 3407, 14176, 58954, 244412, 1010802, 4167621, 17133558, 70278017, 287797888, 1177218237, 4811244031, 19651589669, 80234989720, 327503437323, 1336574600154, 5454075504109, 22254465906164, 90801509373219, 370472833209387

Offset

0,3

Links

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

Wikipedia, Partition of a set

Formula

G.f.: -(16*x^55 +40*x^54 +8*x^53 +74*x^52 -5*x^51 -318*x^50 -184*x^49 -329*x^48 -142*x^47 -724*x^46 -4295*x^45 +135*x^44 +10219*x^43 +11230*x^42 +17694*x^41 -9835*x^40 -58571*x^39 -44920*x^38 -18846*x^37 +77331*x^36 +137586*x^35 -2726*x^34 -66412*x^33 -120019*x^32 -106707*x^31 +110373*x^30 +61244*x^29 -89340*x^28 -166963*x^27 -241737*x^26 -18801*x^25 +183341*x^24 +76875*x^23 -44809*x^22 -194064*x^21 -276159*x^20 -117373*x^19 -3527*x^18 +50167*x^17 +68672*x^16 +6577*x^15 -20654*x^14 -18383*x^13 -13866*x^12 -2815*x^11 +2840*x^10 +1096*x^9 +484*x^8 +288*x^7 -290*x^6 -31*x^5 -4*x^4 -3*x^3 -2*x^2 +5*x -1) / ((x +1)*(x^5 -2*x^3 -2*x +1)*(16*x^40 +8*x^39 -8*x^38 -6*x^37 -25*x^36 -20*x^35 +20*x^34 -447*x^33 -222*x^32 -535*x^31 -399*x^30 +3024*x^29 +1695*x^28 +1438*x^27 +444*x^26 -7664*x^25 -2469*x^24 +1957*x^23 +290*x^22 -50*x^21 -6904*x^20 -7025*x^19 +2502*x^18 +2901*x^17 +352*x^16 -822*x^15 -8224*x^14 -7130*x^13 -2351*x^12 +680*x^11 +2679*x^10 +2620*x^9 +1264*x^8 +408*x^7 +62*x^6 -105*x^5 -48*x^4 -17*x^3 -5*x^2 -x +1)*(x -1)^2*(x^4 +x^3 +x^2 +x -1)^2).

a(n) = A000110(n) for n <= 6.

Crossrefs

Column k=5 of A287417.

Cf. A000110.

Sequence in context: A110038 A343666 A276722 * A287277 A287255 A284727

Adjacent sequences: A287581 A287582 A287583 * A287585 A287586 A287587

Keyword

nonn,easy

Author

Alois P. Heinz, May 26 2017

Status

approved