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.

Showing 1-6 of 6 results.

A248837 Number of length n arrays x(i), i=1..n with x(i) in 0..i and no value appearing more than 3 times.

Original entry on oeis.org

2, 6, 24, 118, 686, 4598, 34872, 295044, 2753958, 28103804, 311216626, 3716341042, 47597786154, 650812077852, 9461423560788, 145724617925326, 2370293673319292, 40600119927220706, 730458115445479734, 13772063820971722638
Offset: 1

Views

Author

R. H. Hardin, Oct 15 2014

Keywords

Comments

Column 3 of A248842.
Essentially the same as A135106. - Georg Fischer, Oct 23 2018

Examples

			Some solutions for n=6
..0....1....0....1....0....0....1....1....1....0....0....0....0....0....0....1
..2....1....0....2....1....1....1....1....1....1....1....0....0....0....1....1
..2....0....0....0....1....1....2....2....0....3....0....2....3....3....2....2
..1....0....3....0....0....1....4....4....1....0....1....1....2....4....4....1
..5....0....2....2....3....4....5....2....2....4....4....0....1....0....5....5
..3....5....3....1....5....2....5....2....5....0....2....5....0....2....0....6

Links

A248836 Number of length n arrays x(i), i=1..n with x(i) in 0..i and no value appearing more than 2 times.

Original entry on oeis.org

1, 2, 6, 22, 96, 482, 2736, 17302, 120576, 917762, 7574016, 67354582, 642041856, 6530291042, 70589700096, 808090395862, 9766250151936, 124258689304322, 1660195646078976, 23239748527125142, 340125128186658816, 5194627679316741602, 82645634692238278656
Offset: 0

Views

Author

R. H. Hardin, Oct 15 2014

Keywords

Comments

Column 2 of A248842

Examples

			Some solutions for n=6
..1....1....1....1....1....0....1....0....0....0....1....0....1....1....1....0
..0....2....2....0....2....2....2....2....2....1....1....1....2....0....0....1
..0....3....0....1....2....1....2....1....1....1....0....3....0....1....2....0
..1....4....0....0....4....2....0....3....3....2....3....3....4....0....0....2
..4....0....3....4....3....4....4....0....1....5....4....2....2....2....2....4
..5....6....4....5....4....0....3....6....6....5....0....2....5....4....4....4

Links

Crossrefs

Cf. A000111, A248842.

Formula

From Seiichi Manyama, Feb 17 2025: (Start)
Conjecture: E.g.f.: 1/(1 - sin(x))^2.
If the above conjecture is correct, the following general term is obtained:
a(n) = Sum_{k=0..n} (k+1)! * i^(n-k) * A136630(n,k), where i is the imaginary unit. (End)
Conjecture from Mikhail Kurkov, Jun 26 2025: (Start)
a(n) = R(n+1,0) where
R(0,0) = 1,
R(n,k) = Sum_{j=0..n-k-1} R(n-1,j) for 0 <= k < n,
R(n,n) = Sum_{j=0..n-1} R(n,j). (End)

Extensions

a(0)=1 prepended by Seiichi Manyama, Feb 17 2025

A248838 Number of length n arrays x(i), i=1..n with x(i) in 0..i and no value appearing more than 4 times.

Original entry on oeis.org

2, 6, 24, 120, 718, 4994, 39556, 351320, 3456742, 37314126, 438366374, 5567209930, 75995663398, 1109556555434, 17252609166736, 284620418911180, 4965138989585412, 91317809653363376, 1765937111915469414
Offset: 1

Views

Author

R. H. Hardin, Oct 15 2014

Keywords

Comments

Column 4 of A248842

Examples

			Some solutions for n=6
..0....1....1....1....0....0....1....0....0....1....0....1....1....0....1....1
..0....2....2....0....0....2....0....2....2....0....2....1....1....2....0....1
..3....2....2....0....2....2....3....2....0....3....1....0....2....2....1....3
..3....0....3....3....3....2....1....2....0....0....0....4....0....1....0....0
..0....5....0....2....2....1....2....2....4....3....2....0....5....4....1....1
..3....4....5....1....6....5....5....5....6....2....1....1....5....4....0....2

Links

A248839 Number of length n arrays x(i), i=1..n with x(i) in 0..i and no value appearing more than 5 times.

Original entry on oeis.org

2, 6, 24, 120, 720, 5038, 40260, 361636, 3606044, 39517182, 472002456, 6102356222, 84896359836, 1264499036118, 20075760897736, 338430468325576, 6037037185793372, 113608224705704476, 2249252806749536964
Offset: 1

Views

Author

R. H. Hardin, Oct 15 2014

Keywords

Comments

Column 5 of A248842

Examples

			Some solutions for n=6
..1....1....0....1....0....1....1....1....0....0....0....1....1....0....0....1
..2....2....2....2....2....1....1....0....2....1....2....2....1....2....2....0
..3....3....0....2....1....3....0....1....0....0....1....0....2....3....0....0
..2....1....2....1....0....4....0....3....0....2....1....1....3....2....1....4
..1....4....4....5....1....2....2....2....5....0....4....4....5....2....0....3
..0....0....2....2....5....3....4....0....5....4....1....4....0....0....5....6

Links

A248840 Number of length n arrays x(i), i=1..n with x(i) in 0..i and no value appearing more than 6 times.

Original entry on oeis.org

2, 6, 24, 120, 720, 5040, 40318, 362804, 3626872, 39874764, 478139586, 6209677488, 86828161058, 1300490408860, 20771844841954, 352424863147204, 6329638315606052, 119970031702245396, 2393022889885984816
Offset: 1

Views

Author

R. H. Hardin, Oct 15 2014

Keywords

Comments

Column 6 of A248842

Examples

			Some solutions for n=6
..0....0....0....0....1....1....0....1....0....1....0....0....1....0....0....0
..1....1....1....1....1....0....0....0....2....0....1....1....1....2....0....1
..1....1....3....3....0....1....2....3....1....0....1....1....0....0....2....3
..0....2....2....1....2....0....2....1....0....4....2....1....2....3....3....4
..1....2....0....2....5....1....5....2....0....1....4....3....0....5....4....1
..2....0....6....3....2....0....1....4....4....2....6....4....3....5....4....3

Links

A248841 Number of length n arrays x(i), i=1..n with x(i) in 0..i and no value appearing more than 7 times.

Original entry on oeis.org

2, 6, 24, 120, 720, 5040, 40320, 362878, 3628706, 39913932, 478928016, 6225275778, 87138262602, 1306763837486, 20901947961712, 355203011199460, 6390875986594862, 121365402664456728, 2425912530967520904
Offset: 1

Views

Author

R. H. Hardin, Oct 15 2014

Keywords

Comments

Column 7 of A248842

Examples

			Some solutions for n=6
..1....0....1....1....0....1....1....0....1....1....1....0....0....1....0....0
..0....2....2....2....1....1....1....2....0....1....0....1....0....1....2....0
..1....2....3....3....0....3....1....2....2....3....1....3....0....2....3....0
..2....3....3....4....0....0....0....3....0....2....3....1....3....3....2....3
..0....1....1....0....4....1....4....2....3....4....1....2....0....3....1....5
..1....5....2....3....3....6....6....5....0....4....0....2....0....2....6....0

Links

Showing 1-6 of 6 results.

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