OFFSET
7,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 7..200
FORMULA
EXAMPLE
a(7) = 1: 1234567.
a(8) = 14: 12345687, 12345786, 12346785, 12356784, 12456783, 13456782, 21345678, 23456781, 31245678, 41235678, 51234678, 61234578, 71234568, 81234567.
MAPLE
b:= proc(u, o, t, k) option remember; `if`(u+o=0, 1,
`if`(t<k-1, add(b(u+j-1, o-j, t+1, k), j=1..o), 0)+
add(b(u-j, o+j-1, 0, k), j=1..u))
end:
a:= n-> b(n, 0, 0, 7)-b(n, 0, 0, 6):
seq(a(n), n=7..30);
MATHEMATICA
b[u_, o_, t_, k_] := b[u, o, t, k] = If[u + o == 0, 1, If[t < k - 1, Sum[b[u + j - 1, o - j, t + 1, k], {j, 1, o}], 0] + Sum[b[u - j, o + j - 1, 0, k], {j, 1, u}]];
a[n_] := b[n, 0, 0, 7] - b[n, 0, 0, 6];
Table[a[n], {n, 7, 30}] (* Jean-François Alcover, Jul 19 2018, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 07 2013
STATUS
approved