cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Previous Showing 11-14 of 14 results.

A292841 Number of sets of nonempty words with a total of n letters over 7-ary alphabet.

Original entry on oeis.org

1, 7, 70, 721, 7042, 67592, 636517, 5904746, 54072137, 489655873, 4390760297, 39030158111, 344244293260, 3014869505704, 26235190722937, 226961433002801, 1952889252127030, 16720135949099562, 142493658202081151, 1209158776638832488, 10219419639669800154
Offset: 0

Views

Author

Alois P. Heinz, Sep 24 2017

Keywords

Crossrefs

Column k=7 of A292804.

Programs

  • Maple
    h:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
          add(h(n-i*j, i-1)*binomial(7^i, j), j=0..n/i)))
        end:
    a:= n-> h(n$2):
    seq(a(n), n=0..30);

Formula

G.f.: Product_{j>=1} (1+x^j)^(7^j).
a(n) ~ 7^n * exp(2*sqrt(n) - 1/2 - c) / (2 * sqrt(Pi) * n^(3/4)), where c = Sum_{m>=2} (-1)^m/(m*(7^(m-1)-1)) = 0.07704538722753681799661640414751144459... - Vaclav Kotesovec, Sep 28 2017

A292842 Number of sets of nonempty words with a total of n letters over 8-ary alphabet.

Original entry on oeis.org

1, 8, 92, 1080, 12070, 132408, 1425372, 15114504, 158210353, 1637612160, 16784647360, 170537275776, 1719204122528, 17209440777600, 171165585295552, 1692447401221248, 16644429470981928, 162875924564677824, 1586486181338263456, 15386713233832145728
Offset: 0

Views

Author

Alois P. Heinz, Sep 24 2017

Keywords

Crossrefs

Column k=8 of A292804.

Programs

  • Maple
    h:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
          add(h(n-i*j, i-1)*binomial(8^i, j), j=0..n/i)))
        end:
    a:= n-> h(n$2):
    seq(a(n), n=0..30);

Formula

G.f.: Product_{j>=1} (1+x^j)^(8^j).
a(n) ~ 8^n * exp(2*sqrt(n) - 1/2 - c) / (2 * sqrt(Pi) * n^(3/4)), where c = Sum_{m>=2} (-1)^m/(m*(8^(m-1)-1)) = 0.066582557989772785055691589503818396917... - Vaclav Kotesovec, Sep 28 2017

A292843 Number of sets of nonempty words with a total of n letters over 9-ary alphabet.

Original entry on oeis.org

1, 9, 117, 1542, 19404, 239481, 2900802, 34609797, 407615175, 4747112731, 54743025339, 625791326688, 7097863351275, 79938092898747, 894514969436076, 9951032414168964, 110103625982603466, 1212181195307220126, 13283829023674846878, 144946503880942833774
Offset: 0

Views

Author

Alois P. Heinz, Sep 24 2017

Keywords

Crossrefs

Column k=9 of A292804.

Programs

  • Maple
    h:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
          add(h(n-i*j, i-1)*binomial(9^i, j), j=0..n/i)))
        end:
    a:= n-> h(n$2):
    seq(a(n), n=0..30);

Formula

G.f.: Product_{j>=1} (1+x^j)^(9^j).
a(n) ~ 9^n * exp(2*sqrt(n) - 1/2 - c) / (2 * sqrt(Pi) * n^(3/4)), where c = Sum_{m>=2} (-1)^m/(m*(9^(m-1)-1)) = 0.058648829660552563553047659756831342987... - Vaclav Kotesovec, Sep 28 2017

A292844 Number of sets of nonempty words with a total of n letters over 10-ary alphabet.

Original entry on oeis.org

1, 10, 145, 2120, 29660, 406752, 5475160, 72591320, 950032770, 12294612660, 157545928646, 2001232474600, 25222164942650, 315640538122100, 3924720693484450, 48514280936275240, 596460638741281825, 7296675024124004450, 88849865885787401525, 1077249149081661058800
Offset: 0

Views

Author

Alois P. Heinz, Sep 24 2017

Keywords

Crossrefs

Column k=10 of A292804.

Programs

  • Maple
    h:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
          add(h(n-i*j, i-1)*binomial(10^i, j), j=0..n/i)))
        end:
    a:= n-> h(n$2):
    seq(a(n), n=0..30);

Formula

G.f.: Product_{j>=1} (1+x^j)^(10^j).
a(n) ~ 10^n * exp(2*sqrt(n) - 1/2 - c) / (2 * sqrt(Pi) * n^(3/4)), where c = Sum_{m>=2} (-1)^m/(m*(10^(m-1)-1)) = 0.05242033574521236673164923513877706425... - Vaclav Kotesovec, Sep 28 2017
Previous Showing 11-14 of 14 results.