A360650 Number of sets of nonempty words over binary alphabet with a total of n letters of which 2 are the first letter.

0, 0, 1, 6, 16, 37, 73, 133, 227, 370, 580, 881, 1305, 1890, 2687, 3756, 5175, 7037, 9460, 12582, 16577, 21649, 28048, 36070, 46072, 58474, 73778, 92574, 115559, 143551, 177510, 218556, 267997, 327355, 398394, 483162, 584023, 703708, 845361, 1012600, 1209573

Offset: 0

Author

Alois P. Heinz, Feb 15 2023

Keywords

• nonn

Examples

			a(2) = 1: {aa}.
a(3) = 6: {aab}, {aba}, {baa}, {a,ab}, {a,ba}, {aa,b}.
a(4) = 16: {aabb}, {abab}, {abba}, {baab}, {baba}, {bbaa}, {a,abb}, {a,bab}, {a,bba}, {aa,bb}, {aab,b}, {ab,ba}, {aba,b}, {b,baa}, {a,ab,b}, {a,b,ba}.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Column k=2 of A360634.

Programs

Maple

g:= proc(n, i, j) option remember; convert(series(`if`(j=0, 1,
      `if`(i<0, 0, add(g(n, i-1, j-k)*x^(i*k)*binomial(
          binomial(n, i), k), k=0..j))), x, 3), polynom)
    end:
b:= proc(n, i) option remember; convert(series(`if`(n=0, 1, `if`(i<1, 0,
      add(b(n-i*j, i-1)*g(i$2, j), j=0..n/i))), x, 3), polynom)
    end:
a:= n-> coeff(b(n$2), x, 2):
seq(a(n), n=0..45);

Formula

a(n) = A360634(n,2).