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 1-4 of 4 results.

A215293 Number of permutations of 0..floor((n*n-2)/2) on odd squares of an n X n array such that each row and column of odd squares is increasing.

Original entry on oeis.org

1, 2, 6, 280, 23100, 85765680, 577185873264, 346915095471584640, 381134230556959188429120, 62144711688730139887005809020800, 18592619468814454675301397184588597886400, 1236552808693429892089668394551052130596983991526400, 151213938214745201135492692441902799026853717717324113365952000
Offset: 1

Views

Author

R. H. Hardin, Aug 07 2012

Keywords

Examples

			Some solutions for n=5
..x..0..x..4..x....x..4..x..6..x....x..1..x..6..x....x..0..x..6..x
..1..x..3..x..7....0..x..1..x..9....0..x..2..x..3....3..x..4..x..9
..x..2..x..5..x....x..5..x..8..x....x..7..x..8..x....x..1..x..7..x
..8..x..9..x.10....2..x..3..x.10....4..x..5..x.11....5..x..8..x.11
..x..6..x.11..x....x..7..x.11..x....x..9..x.10..x....x..2..x.10..x
		

Crossrefs

Diagonal of A215297.
Cf. A060854.

Formula

T(n,k) = A060854(f1,f2)*A060854(f2,f1)*binomial(f1*f2+f2*f1,f1*f2) with f1 = floor(n/2) and f2 = floor((n+1)/2).

A215294 Number of permutations of 0..floor((n*3-2)/2) on odd squares of an n X 3 array such that each row and column of odd squares is increasing.

Original entry on oeis.org

1, 3, 6, 30, 70, 420, 1050, 6930, 18018, 126126, 336336, 2450448, 6651216, 49884120, 137181330, 1051723530, 2921454250, 22787343150, 63804560820, 504636071940, 1422156202740, 11377249621920, 32235540595440, 260363981732400
Offset: 1

Views

Author

R. H. Hardin, Aug 07 2012

Keywords

Comments

a(n) is number of symmetric standard Young tableaux of shape (n,n,n). - Ran Pan, May 21 2015

Examples

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

Crossrefs

Column 3 of A215297.
Cf. A060693.

Programs

  • Maple
    a := n -> `if`(irem(n, 2) = 0, ((1/2)*n+1)*factorial((3/2)*n)/ (factorial((1/2)*n+1)^2*factorial((1/2)*n)), factorial((3/2)*n+3/2)/ (factorial((1/2)*n+1/2)^3*((9/2)*n+3/2))): # Peter Luschny, Sep 30 2018

Formula

a(n) = A060854(1,f3)*A060854(2,f4)*binomial(1*f3+2*f4,1*f3) where f3 = floor((n+1)/2), f4 = floor(n/2).
a(n) = e(n) if n even otherwise o(n), where e(n) = 6*Gamma((3*n)/2)/((2 + n)*Gamma(1 + n/2)^2*Gamma(n/2)) and o(n) = (1 + n)*Gamma(1/2 + (3*n)/2)/(2*Gamma((3 + n)/2)^3). - Peter Luschny, Sep 30 2018

A215295 Number of permutations of 0..floor((n*5-2)/2) on odd squares of an nX5 array such that each row and column of odd squares is increasing.

Original entry on oeis.org

1, 10, 70, 2100, 23100, 1051050, 14294280, 814773960, 12547518984, 824551247520, 13781785137120, 999179422441200, 17699749768958400, 1379105502831342000, 25513451802379827000, 2100607531729272423000, 40191624107086745693400
Offset: 1

Views

Author

R. H. Hardin Aug 07 2012

Keywords

Comments

Column 5 of A215297

Examples

			Some solutions for n=5
..x..2..x..6..x....x..1..x..5..x....x..0..x..5..x....x..0..x..2..x
..0..x..3..x..4....0..x..2..x..7....2..x..4..x.10....3..x..6..x..8
..x..5..x.10..x....x..3..x..9..x....x..1..x..8..x....x..1..x..7..x
..1..x..7..x..8....4..x..6..x.11....6..x..7..x.11....4..x..9..x.11
..x..9..x.11..x....x..8..x.10..x....x..3..x..9..x....x..5..x.10..x
		

Formula

f3=floor((n+1)/2)
f4=floor(n/2)
a(n) = A060854(2,f3)*A060854(3,f4)*binomial(2*f3+3*f4,2*f3)

A215296 Number of permutations of 0..floor((n*7-2)/2) on odd squares of an nX7 array such that each row and column of odd squares is increasing.

Original entry on oeis.org

1, 35, 1050, 210210, 14294280, 5703417720, 577185873264, 337653735859440, 43364386933948080, 32436561426593163840, 4886336289191784467040, 4340695403565368534887200, 733267473530864041786302000
Offset: 1

Views

Author

R. H. Hardin Aug 07 2012

Keywords

Comments

Column 7 of A215297

Examples

			Some solutions for n=3
..x..0..x..1..x..3..x....x..0..x..2..x..5..x....x..0..x..1..x..3..x
..2..x..4..x..6..x..9....3..x..6..x..8..x..9....5..x..6..x..8..x..9
..x..5..x..7..x..8..x....x..1..x..4..x..7..x....x..2..x..4..x..7..x
		

Formula

f3=floor((n+1)/2)
f4=floor(n/2)
a(n) = A060854(3,f3)*A060854(4,f4)*binomial(3*f3+4*f4,3*f3)
Showing 1-4 of 4 results.