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.
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
Offset: 0
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.