A287278 Number of set partitions of [n] such that for each block all absolute differences between consecutive elements are <= six.

1, 1, 2, 5, 15, 52, 203, 877, 3937, 18162, 85347, 405803, 1942918, 9339084, 45003444, 217201380, 1049271992, 5071767524, 24523356660, 118602078194, 573667951966, 2774998925735, 13424115897227, 64941326312858, 314169695256551, 1519889795069445, 7352969270282127

Offset

0,3

Links

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

Pierpaolo Natalini, Paolo Emilio Ricci, New Bell-Sheffer Polynomial Sets, Axioms 2018, 7(4), 71.

Wikipedia, Partition of a set

Formula

G.f.: -(x^31 +2*x^30 +3*x^29 +4*x^28 +6*x^27 -24*x^26 -46*x^25 -60*x^24 -81*x^23 -129*x^22 +156*x^21 +265*x^20 +224*x^19 +350*x^18 +617*x^17 -425*x^16 -531*x^15 -161*x^14 -567*x^13 -806*x^12 +462*x^11 +401*x^10 +85*x^9 +198*x^8 +227*x^7 -185*x^6 -35*x^5 -4*x^4 -5*x^3 -4*x^2 +6*x-1) / (x^32 +x^31 +x^30 +x^29 +x^28 -32*x^27 -24*x^26 -15*x^25 -23*x^24 -23*x^23 +329*x^22 +141*x^21 -20*x^20 +164*x^19 +101*x^18 -1243*x^17 -175*x^16 +277*x^15 -495*x^14 +8*x^13 +1536*x^12 +17*x^11 -235*x^10 +121*x^9 -115*x^8 -447*x^7 +152*x^6 +32*x^5 +x^4 +5*x^3 +9*x^2 -7*x+1).

a(n) = A287214(n,6).

a(n) = A000110(n) for n <= 7.

Crossrefs

Column k=6 of A287214.

Cf. A000110.

Sequence in context: A343667 A276723 A287585 * A287256 A287668 A099262

Adjacent sequences: A287275 A287276 A287277 * A287279 A287280 A287281

Keyword

nonn,easy

Author

Alois P. Heinz, May 22 2017

Status

approved