A242323 Number of binary words of length n that contain all 32 5-bit words as (possibly overlapping) contiguous subwords.

65536, 352256, 1442816, 5313536, 18323520, 60481632, 192562808, 593792608, 1782459992, 5221699004, 14967607810, 42060446246, 116067269324

Offset: 36

Author

Alois P. Heinz, May 10 2014

Keywords

• nonn
• more

Examples

			a(36) = 65536: 000001000110010100111010110111110000, ... .
		

Links

• Eric Weisstein's World of Mathematics, Coin Tossing

Crossrefs

Cf. A001146, A052944, A242167, A242206, A242257.

Programs

Maple

b:= proc(n, t, s) option remember; `if`(s={}, 2^n,
      `if`(nops(s)>n, 0, b(n-1, irem(2*t, 16), s minus {2*t})
        +b(n-1, irem(2*t+1, 16), s minus {2*t+1})))
    end:
a:= n-> add(b(n-4, j, {$0..31}), j=0..15):
seq(a(n), n=36..37);

Mathematica

b[n_, t_, s_] := b[n, t, s] = If[s == {}, 2^n,
   If[Length[s] > n, 0, b[n-1, Mod[2*t, 16], s~Complement~{2*t}] +
   b[n-1, Mod[2*t+1, 16], s~Complement~{2*t+1}]]];
a[n_] := Sum[b[n-4, j, Range[0, 31]], {j, 0, 15}];
Table[a[n], {n, 36, 39}] (* Jean-François Alcover, Sep 06 2022, after Alois P. Heinz *)

Extensions

a(44)-a(48) from Alois P. Heinz, Feb 27 2015