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 1-5 of 5 results.

A264635 Number of n X 1 arrays of permutations of 0..n*1-1 with rows nondecreasing modulo 2 and columns nondecreasing modulo 4.

Original entry on oeis.org

1, 1, 1, 1, 2, 4, 8, 16, 48, 144, 432, 1296, 5184, 20736, 82944, 331776, 1658880, 8294400, 41472000, 207360000, 1244160000, 7464960000, 44789760000, 268738560000, 1881169920000, 13168189440000, 92177326080000, 645241282560000, 5161930260480000
Offset: 1

Views

Author

R. H. Hardin, Nov 19 2015

Keywords

Examples

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

Links

Crossrefs

Column 1 of A264638.
Column k=4 of A275062.

Programs

  • Mathematica
    Table[Product[Floor[(n + i)/4]!, {i, 0, 3}], {n, 1, 30}] (* Vaclav Kotesovec, Oct 02 2018 *)

Formula

a(n) = Product_{i=0..3} floor((n+i)/4)!. - Alois P. Heinz, Jul 12 2016
a(n) ~ Pi^(3/2) * n^(3/2) * n! / 2^(2*n + 5/2). - Vaclav Kotesovec, Oct 02 2018
Sum_{n>0} floor((n-1)/4)/a(n) = 1. - Peter McNair, May 29 2022

A264636 Number of nX2 arrays of permutations of 0..n*2-1 with rows nondecreasing modulo 2 and columns nondecreasing modulo 4.

Original entry on oeis.org

1, 3, 16, 128, 1152, 12960, 269568, 6635520, 165888000, 4561920000, 209018880000, 10480803840000, 513559388160000, 26454892584960000, 2106067546275840000
Offset: 1

Views

Author

R. H. Hardin, Nov 19 2015

Keywords

Comments

Column 2 of A264638.

Examples

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

Crossrefs

Cf. A264638.

A264637 Number of nX3 arrays of permutations of 0..n*3-1 with rows nondecreasing modulo 2 and columns nondecreasing modulo 4.

Original entry on oeis.org

2, 28, 960, 46656, 4561920, 829440000, 218972160000, 73903104000000
Offset: 1

Views

Author

R. H. Hardin, Nov 19 2015

Keywords

Comments

Column 3 of A264638.

Examples

			Some solutions for n=4
..8..0..9....8..4..0....4..8..0....4.10..9....0..4..8....0..4..9....2..8..4
..6..4..1...10..5..9...10..6..1....0..6..5....6..1..5...10..8..5...10..0..5
.10..2..5....2..6..1....2..3..9....8..2..1....2..9..7....2..7..1....6.11..1
..3.11..7....7..3.11...11..7..5....3..7.11...10.11..3....6.11..3....3..7..9

Crossrefs

Cf. A264638.

A264639 Number of 2 X n arrays of permutations of 0..n*2-1 with rows nondecreasing modulo 2 and columns nondecreasing modulo 4.

Original entry on oeis.org

1, 3, 28, 400, 7776, 229392, 9082368, 481406976, 30249676800, 2458667520000, 229405685760000
Offset: 1

Views

Author

R. H. Hardin, Nov 19 2015

Keywords

Comments

Row 2 of A264638.

Examples

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

Crossrefs

Cf. A264638.

A264640 Number of 3Xn arrays of permutations of 0..n*3-1 with rows nondecreasing modulo 2 and columns nondecreasing modulo 4.

Original entry on oeis.org

1, 16, 960, 107568, 21565440, 10027929600, 7163873280000
Offset: 1

Views

Author

R. H. Hardin, Nov 19 2015

Keywords

Comments

Row 3 of A264638.

Examples

			Some solutions for n=4
..0..4..6..8....8..6..0..1....4..2..8..1....8..4..9..1....0..8..5..1
..2..1.11..9....4..2..5..9....0..6.10..9....0..6.10..5....4..6.10..9
.10..5..3..7...10..7.11..3...11..3..7..5....2..7.11..3....2..7.11..3

Crossrefs

Cf. A264638.
Showing 1-5 of 5 results.

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