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

0,4

Links

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

Formula

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

Example

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}.

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);

Crossrefs

Column k=2 of A360634.

Sequence in context: A237601 A372669 A064602 * A346375 A058272 A049712

Adjacent sequences: A360647 A360648 A360649 * A360651 A360652 A360653

Keyword

nonn

Author

Alois P. Heinz, Feb 15 2023

Status

approved