A287583 - OEIS

%I #7 May 26 2017 21:00:25

%S 1,1,2,5,15,52,187,677,2439,8707,30871,108696,380653,1328193,4623194,

%T 16065161,55763738,193430602,670683122,2324853720,8057594663,

%U 27923827498,96765523944,335314355594,1161917842116,4026187435945,13951144657754,48341945365173

%N 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.

%H Alois P. Heinz, <a href="/A287583/b287583.txt">Table of n, a(n) for n = 0..1000</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>

%H <a href="/index/Rec#order_24">Index entries for linear recurrences with constant coefficients</a>, 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)

%F 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).

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

%Y Column k=4 of A287417.

%Y Cf. A000110.

%K nonn,easy

%O 0,3

%A _Alois P. Heinz_, May 26 2017