OFFSET
0,13
COMMENTS
The five consecutive patterns that occur at least once each are 101010, 101100, 110010, 110100, 111000. Here 1=Up=(1,1), 0=Down=(1,-1).
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..300
EXAMPLE
a(12) = 12: 101010110010110100111000, 101010110010111000110100, 101100101010110100111000, 101100101010111000110100, 110100101010110010111000, 110100101100101010111000, 110100111000101010110010, 110100111000101100101010, 111000101010110010110100, 111000101100101010110100, 111000110100101010110010, 111000110100101100101010.
Here 1=Up=(1,1), 0=Down=(1,-1).
MAPLE
b:= proc(x, y, l) option remember; local m; m:= min(l[]);
`if`(y>x or y<0 or 7-m>x, 0, `if`(x=0, 1,
b(x-1, y+1, [[2, 3, 4, 4, 2, 2, 7][l[1]],
[2, 3, 3, 5, 3, 2, 7][l[2]], [2, 3, 3, 2, 6, 3, 7][l[3]],
[2, 2, 4, 5, 2, 4, 7][l[4]], [2, 2, 4, 2, 6, 2, 7][l[5]]])+
b(x-1, y-1, [[1, 1, 1, 5, 6, 7, 7][l[1]],
[1, 1, 4, 1, 6, 7, 7][l[2]], [1, 1, 4, 5, 1, 7, 7][l[3]],
[1, 3, 1, 3, 6, 7, 7][l[4]], [1, 3, 1, 5, 1, 7, 7][l[5]]])))
end:
a:= n-> b(2*n, 0, [1$5]):
seq(a(n), n=0..35);
MATHEMATICA
b[x_, y_, l_] := b[x, y, l] = Module[{m = Min[l]},
If[y>x || y<0 || 7-m>x, 0, If[x == 0, 1,
b[x-1, y+1, MapIndexed[#1[[l[[#2[[1]] ]] ]]&,
{{2, 3, 4, 4, 2, 2, 7},
{2, 3, 3, 5, 3, 2, 7},
{2, 3, 3, 2, 6, 3, 7},
{2, 2, 4, 5, 2, 4, 7},
{2, 2, 4, 2, 6, 2, 7}}]]] +
b[x-1, y-1, MapIndexed[#1[[l[[#2[[1]] ]] ]]&,
{{1, 1, 1, 5, 6, 7, 7},
{1, 1, 4, 1, 6, 7, 7},
{1, 1, 4, 5, 1, 7, 7},
{1, 3, 1, 3, 6, 7, 7},
{1, 3, 1, 5, 1, 7, 7}}]]]];
a[n_] := b[2n, 0, {1, 1, 1, 1, 1}];
a /@ Range[0, 35] (* Jean-François Alcover, Jan 26 2021, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jun 16 2014
STATUS
approved