A322879 - OEIS

%I #4 Dec 29 2018 15:50:15

%S 0,1,35,413,3709,30396,242366,1934021,15653524,129267234,1091892025,

%T 9444993005,83722879838,760771479660,7087056828919,67674638461955,

%U 662248199987728,6638947646238102,68153572265860585,716151632403862252,7699437833837232406

%N Number of set partitions of [n] such that the maximal absolute difference between the least elements of consecutive blocks equals six.

%H Alois P. Heinz, <a href="/A322879/b322879.txt">Table of n, a(n) for n = 6..581</a>

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

%F a(n) = A287256(n) - A287255(n).

%p b:= proc(n, k, m, l) option remember; `if`(n<1, 1,

%p      `if`(l-n>k, 0, b(n-1, k, m+1, n))+m*b(n-1, k, m, l))

%p     end:

%p A:= (n, k)-> b(n-1, min(k, n-1), 1, n):

%p a:= n-> (k-> A(n, k)-A(n, k-1))(6):

%p seq(a(n), n=6..30);

%Y Column k=6 of A287215.

%Y Cf. A287255, A287256.

%K nonn

%O 6,3

%A _Alois P. Heinz_, Dec 29 2018