A319501 -id:A319501 - cp's OEIS frontend

A320208 Number of sets of nonempty words with a total of n letters over septenary alphabet such that all letters occur at least once in the set.

37633, 1366057, 28969248, 470004045, 6470660266, 79706067707, 906335330250, 9706198156760, 99243640018075, 978284068984075, 9363362648969343, 87485517250169934, 801259222264152813, 7216852772737393058, 64088034265985397794, 562287261308092526759

Offset: 7

Alois P. Heinz, Oct 07 2018

nonn

Alois P. Heinz, Table of n, a(n) for n = 7..1000

Column k=7 of A319501.

Cf. A320217.

h:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
      add(h(n-i*j, i-1, k)*binomial(k^i, j), j=0..n/i)))
    end:
a:= n-> (k-> add((-1)^i*binomial(k, i)*h(n$2, k-i), i=0..k))(7):
seq(a(n), n=7..25);

A320209 Number of sets of nonempty words with a total of n letters over octonary alphabet such that all letters occur at least once in the set.

Original entry on oeis.org

394353, 18235680, 484092688, 9697863856, 163046201132, 2430540970008, 33194557467204, 424251626739144, 5148887208055692, 59963231946871288, 675318621308265328, 7398542789316786184, 79210967706138213860, 831754864387299725168, 8590788276593760698232

Offset: 8

Alois P. Heinz, Oct 07 2018

nonn

Alois P. Heinz, Table of n, a(n) for n = 8..1000

Column k=8 of A319501.

Cf. A320218.

h:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
      add(h(n-i*j, i-1, k)*binomial(k^i, j), j=0..n/i)))
    end:
a:= n-> (k-> add((-1)^i*binomial(k, i)*h(n$2, k-i), i=0..k))(8):
seq(a(n), n=8..25);

A320210 Number of sets of nonempty words with a total of n letters over nonary alphabet such that all letters occur at least once in the set.

Original entry on oeis.org

4596553, 263460321, 8549512506, 207037303758, 4169086763787, 73865658618900, 1191183607371897, 17876336340787308, 253521082577243286, 3435636331820210328, 44859666267675306756, 567955878004442678319, 7007036376866803617768, 84571686324119453047650

Offset: 9

Alois P. Heinz, Oct 07 2018

nonn

Alois P. Heinz, Table of n, a(n) for n = 9..1000

Column k=9 of A319501.

Cf. A320219.

h:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
      add(h(n-i*j, i-1, k)*binomial(k^i, j), j=0..n/i)))
    end:
a:= n-> (k-> add((-1)^i*binomial(k, i)*h(n$2, k-i), i=0..k))(9):
seq(a(n), n=9..25);

A320211 Number of sets of nonempty words with a total of n letters over denary alphabet such that all letters occur at least once in the set.

Original entry on oeis.org

58941091, 4097382940, 159454061270, 4587784661870, 108909499300650, 2259736176893470, 42433681634931005, 737876928284127870, 12073172284265618005, 188049325030487680920, 2812707955072045999940, 40672129029056125818340, 571583937930987524954470

Offset: 10

Alois P. Heinz, Oct 07 2018

nonn

Alois P. Heinz, Table of n, a(n) for n = 10..975

Column k=10 of A319501.

Cf. A320220.

h:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
      add(h(n-i*j, i-1, k)*binomial(k^i, j), j=0..n/i)))
    end:
a:= n-> (k-> add((-1)^i*binomial(k, i)*h(n$2, k-i), i=0..k))(10):
seq(a(n), n=10..25);

A320203 Number of sets of nonempty words with a total of n letters over binary alphabet such that all letters occur at least once in the set.

Original entry on oeis.org

3, 12, 38, 110, 302, 806, 2109, 5450, 13917, 35224, 88464, 220608, 546734, 1347290, 3302716, 8057268, 19568800, 47329156, 114025658, 273709580, 654765164, 1561257760, 3711372761, 8797021430, 20794198251, 49024480496, 115292809466, 270495295124, 633186396954

Offset: 2

Alois P. Heinz, Oct 07 2018

nonn

			a(2) = 3: {ab}, {ba}, {a,b}.
a(3) = 12: {aab}, {aba}, {abb}, {baa}, {bab}, {bba}, {a,ab}, {a,ba}, {a,bb}, {aa,b}, {ab,b}, {b,ba}.
a(4) = 38: {aaab}, {aaba}, {aabb}, {abaa}, {abab}, {abba}, {abbb}, {baaa}, {baab}, {baba}, {babb}, {bbaa}, {bbab}, {bbba}, {a,aab}, {a,aba}, {a,abb}, {a,baa}, {a,bab}, {a,bba}, {a,bbb}, {aa,ab}, {aa,ba}, {aa,bb}, {aaa,b}, {aab,b}, {ab,ba}, {ab,bb}, {aba,b}, {abb,b}, {b,baa}, {b,bab}, {b,bba}, {ba,bb}, {a,aa,b}, {a,ab,b}, {a,b,ba}, {a,b,bb}.

Alois P. Heinz, Table of n, a(n) for n = 2..1000

Column k=2 of A319501.

h:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
      add(h(n-i*j, i-1, k)*binomial(k^i, j), j=0..n/i)))
    end:
a:= n-> (k-> add((-1)^i*binomial(k, i)*h(n$2, k-i), i=0..k))(2):
seq(a(n), n=2..35);

cp's OEIS Frontend

A320208 Number of sets of nonempty words with a total of n letters over septenary alphabet such that all letters occur at least once in the set.

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Maple

A320209 Number of sets of nonempty words with a total of n letters over octonary alphabet such that all letters occur at least once in the set.

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Author

Keywords

Links

Crossrefs

Programs

Maple

A320210 Number of sets of nonempty words with a total of n letters over nonary alphabet such that all letters occur at least once in the set.

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

A320211 Number of sets of nonempty words with a total of n letters over denary alphabet such that all letters occur at least once in the set.

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

A320203 Number of sets of nonempty words with a total of n letters over binary alphabet such that all letters occur at least once in the set.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple