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 1-10 of 10 results.

A215870 T(n,k) = Number of permutations of 0..floor((n*k-2)/2) on odd squares of an n X k array such that each row, column, diagonal and (downwards) antidiagonal of odd squares is increasing.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 5, 4, 4, 1, 1, 1, 1, 5, 12, 10, 4, 1, 1, 1, 1, 14, 29, 78, 20, 8, 1, 1, 1, 1, 14, 110, 262, 189, 50, 8, 1, 1, 1, 1, 42, 290, 3001, 1642, 1233, 100, 16, 1, 1, 1, 1, 42, 1274, 11694, 26451, 15485, 2988, 250, 16, 1, 1, 1, 1, 132
Offset: 1

Views

Author

R. H. Hardin, Aug 25 2012

Keywords

Comments

Table starts
.1.1.1..1....1......1.......1.........1.........1..........1........1
.1.1.1..2....2......5.......5........14........14.........42.......42
.1.1.1..2....4.....12......29.......110.......290.......1274.....3532
.1.1.1..4...10.....78.....262......3001.....11694.....170594...727846
.1.1.1..4...20....189....1642.....26451....307874....7027942.98057806
.1.1.1..8...50...1233...15485....767560..14296434.1124811332
.1.1.1..8..100...2988...97289...6812794.386699176
.1.1.1.16..250..19494..918637.198409297
.1.1.1.16..500..47241.5772013
.1.1.1.32.1250.308205
.1.1.1.32.2500
.1.1.1.64

Examples

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

Links

Crossrefs

Column 5 is A026395(n-1).
Row 2 is A000108(floor(n/2)).
Even squares: A215788.

Formula

Empirical for column k:
k=4: a(n) = 2*a(n-2), A016116.
k=5: a(n) = 5*a(n-2) for n>3, A026395.
k=6: a(n) = 16*a(n-2) -3*a(n-4), A215866.
k=7: a(n) = 61*a(n-2) -99*a(n-4) -2*a(n-6), A215867.
k=8: a(n) = 272*a(n-2) -3439*a(n-4) -3336*a(n-6) +140*a(n-8).
k=9: a(n) = 1385*a(n-2) -131648*a(n-4) -318070*a(n-6) -4160916*a(n-8) -1097892*a(n-10) +648*a(n-12).

A215784 Number of permutations of 0..floor((n*6-1)/2) on even squares of an n X 6 array such that each row, column, diagonal and (downwards) antidiagonal of even squares is increasing.

Original entry on oeis.org

1, 2, 12, 29, 189, 458, 2988, 7241, 47241, 114482, 746892, 1809989, 11808549, 28616378, 186696108, 452432081, 2951712081, 7153064162, 46667304972, 113091730349, 737821743309, 1788008493098, 11665145978028, 28268860698521
Offset: 1

Views

Author

R. H. Hardin, Aug 23 2012

Keywords

Comments

Column 6 of A215788.

Examples

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

Links

Crossrefs

Cf. A215788.

Formula

Empirical: a(n) = 16*a(n-2) - 3*a(n-4).
Empirical g.f.: x*(1 + 3*x)*(1 - x - x^2) / (1 - 16*x^2 + 3*x^4). - Colin Barker, Jul 23 2018

A215785 Number of permutations of 0..floor((n*7-1)/2) on even squares of an n X 7 array such that each row, column, diagonal and (downwards) antidiagonal of even squares is increasing.

Original entry on oeis.org

1, 5, 42, 262, 2465, 15485, 146205, 918637, 8674386, 54503318, 514658321, 3233726365, 30535100957, 191859642509, 1811672635826, 11383190276278, 107488026474001, 675374034791837, 6377352953765373, 40070496565665517
Offset: 1

Views

Author

R. H. Hardin, Aug 23 2012

Keywords

Comments

Column 7 of A215788.

Examples

			Some solutions for n=4:
..0..x..1..x..2..x..3....0..x..1..x..3..x..4....0..x..1..x..2..x..6
..x..4..x..6..x..7..x....x..2..x..5..x..6..x....x..3..x..4..x..8..x
..5..x..8..x..9..x.12....7..x..8..x..9..x.10....5..x..7..x.10..x.12
..x.10..x.11..x.13..x....x.11..x.12..x.13..x....x..9..x.11..x.13..x

Links

Crossrefs

Cf. A215788.

Formula

Empirical: a(n) = 61*a(n-2) - 99*a(n-4) - 2*a(n-6).
Empirical g.f.: x*(1 + 5*x - 19*x^2 - 43*x^3 + 2*x^4 - 2*x^5) / (1 - 61*x^2 + 99*x^4 + 2*x^6). - Colin Barker, Jul 23 2018

A215786 Number of permutations of 0..floor((n*8-1)/2) on even squares of an nX8 array such that each row, column, diagonal and (downwards) antidiagonal of even squares is increasing.

Original entry on oeis.org

1, 5, 110, 932, 26451, 234217, 6812794, 60485308, 1761748159, 15643423061, 455678075546, 4046220880948, 117863060852067, 1046572601513969, 30485799411892266, 270700616010831020, 7885286478349158743
Offset: 1

Views

Author

R. H. Hardin Aug 23 2012

Keywords

Comments

Column 8 of A215788

Examples

			Some solutions for n=4
..0..x..1..x..3..x..7..x....0..x..1..x..2..x..3..x....0..x..1..x..2..x..5..x
..x..2..x..4..x..9..x.10....x..4..x..6..x..7..x..8....x..3..x..4..x..7..x.11
..5..x..6..x.11..x.12..x....5..x..9..x.10..x.12..x....6..x..8..x..9..x.13..x
..x..8..x.13..x.14..x.15....x.11..x.13..x.14..x.15....x.10..x.12..x.14..x.15

Links

Formula

Empirical: a(n) = 272*a(n-2) -3439*a(n-4) -3336*a(n-6) +140*a(n-8)

A215787 Number of permutations of 0..floor((n*9-1)/2) on even squares of an nX9 array such that each row, column, diagonal and (downwards) antidiagonal of even squares is increasing.

Original entry on oeis.org

1, 14, 462, 11694, 530429, 14296434, 673507749, 18255280444, 862827082115, 23397688110992, 1106178923600669, 29997930933948284, 1418251919293188195, 38461009542931961924, 1818375422885354065137, 49311812528326463481148
Offset: 1

Views

Author

R. H. Hardin Aug 23 2012

Keywords

Comments

Column 9 of A215788

Examples

			Some solutions for n=4
..0..x..1..x..3..x..6..x..8....0..x..1..x..2..x..6..x.11
..x..2..x..5..x.10..x.13..x....x..3..x..5..x..8..x.12..x
..4..x..7..x.11..x.14..x.15....4..x..7..x.10..x.14..x.16
..x..9..x.12..x.16..x.17..x....x..9..x.13..x.15..x.17..x

Links

Formula

Empirical: a(n) = 1385*a(n-2) -131648*a(n-4) -318070*a(n-6) -4160916*a(n-8) -1097892*a(n-10) +648*a(n-12)

A215789 Number of permutations of 0..floor((3*n-1)/2) on even squares of an 3*n array such that each row, column, diagonal and (downwards) antidiagonal of even squares is increasing.

Original entry on oeis.org

1, 1, 1, 2, 5, 12, 42, 110, 462, 1274, 6006, 17136, 87516, 255816, 1385670, 4124406, 23371634, 70549050, 414315330, 1264752060, 7646001090, 23555382240, 145862174640, 452806924752, 2861142656400, 8939481277552, 57468093927120
Offset: 1

Views

Author

R. H. Hardin Aug 23 2012

Keywords

Comments

Row 3 of A215788

Examples

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

A215790 Number of permutations of 0..floor((4*n-1)/2) on even squares of an 4*n array such that each row, column, diagonal and (downwards) antidiagonal of even squares is increasing.

Original entry on oeis.org

1, 1, 1, 2, 10, 29, 262, 932, 11694, 46988, 727846, 3166688, 56797272, 261286670, 5219906670, 25024705056
Offset: 1

Views

Author

R. H. Hardin Aug 23 2012

Keywords

Comments

Row 4 of A215788

Examples

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

A215791 Number of permutations of 0..floor((5*n-1)/2) on even squares of an 5*n array such that each row, column, diagonal and (downwards) antidiagonal of even squares is increasing.

Original entry on oeis.org

1, 1, 1, 4, 25, 189, 2465, 26451, 530429, 7027942, 187205626, 2850280812
Offset: 1

Views

Author

R. H. Hardin, Aug 23 2012

Keywords

Examples

			Some solutions for n=5:
..0..x..1..x..4....0..x..1..x..4....0..x..1..x..3....0..x..1..x..3
..x..2..x..5..x....x..2..x..5..x....x..2..x..4..x....x..2..x..5..x
..3..x..6..x..8....3..x..6..x..8....5..x..6..x..8....4..x..6..x..8
..x..7..x..9..x....x..7..x.10..x....x..7..x..9..x....x..7..x..9..x
.10..x.11..x.12....9..x.11..x.12...10..x.11..x.12...10..x.11..x.12

Crossrefs

Row 5 of A215788.

A215792 Number of permutations of 0..floor((6*n-1)/2) on even squares of an 6*n array such that each row, column, diagonal and (downwards) antidiagonal of even squares is increasing.

Original entry on oeis.org

1, 1, 1, 4, 50, 458, 15485, 234217, 14296434, 297246092, 26970790176
Offset: 1

Views

Author

R. H. Hardin Aug 23 2012

Keywords

Comments

Row 6 of A215788

Examples

			Some solutions for n=5
..0..x..1..x..4....0..x..1..x..2....0..x..1..x..4....0..x..1..x..2
..x..2..x..5..x....x..3..x..4..x....x..2..x..5..x....x..3..x..4..x
..3..x..6..x..8....5..x..6..x..7....3..x..6..x..8....5..x..6..x..8
..x..7..x.10..x....x..8..x..9..x....x..7..x..9..x....x..7..x..9..x
..9..x.11..x.13...10..x.11..x.13...10..x.11..x.13...10..x.11..x.12
..x.12..x.14..x....x.12..x.14..x....x.12..x.14..x....x.13..x.14..x

A215793 Number of permutations of 0..floor((7*n-1)/2) on even squares of an 7*n array such that each row, column, diagonal and (downwards) antidiagonal of even squares is increasing.

Original entry on oeis.org

1, 1, 1, 8, 125, 2988, 146205, 6812794, 673507749, 48337803306
Offset: 1

Views

Author

R. H. Hardin Aug 23 2012

Keywords

Comments

Row 7 of A215788

Examples

			Some solutions for n=4
..0..x..1..x....0..x..1..x....0..x..1..x....0..x..1..x....0..x..1..x
..x..2..x..4....x..2..x..3....x..2..x..3....x..2..x..4....x..2..x..4
..3..x..5..x....4..x..5..x....4..x..5..x....3..x..5..x....3..x..5..x
..x..6..x..7....x..6..x..7....x..6..x..7....x..6..x..8....x..6..x..8
..8..x..9..x....8..x..9..x....8..x..9..x....7..x..9..x....7..x..9..x
..x.10..x.12....x.10..x.12....x.10..x.11....x.10..x.12....x.10..x.11
.11..x.13..x...11..x.13..x...12..x.13..x...11..x.13..x...12..x.13..x
Showing 1-10 of 10 results.

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