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.

A215788 T(n,k)=Number of permutations of 0..floor((n*k-1)/2) on even squares of an nXk array such that each row, column, diagonal and (downwards) antidiagonal of even squares is increasing.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 5, 2, 1, 1, 1, 1, 5, 12, 10, 4, 1, 1, 1, 1, 5, 42, 29, 25, 4, 1, 1, 1, 1, 14, 110, 262, 189, 50, 8, 1, 1, 1, 1, 14, 462, 932, 2465, 458, 125, 8, 1, 1, 1, 1, 42, 1274, 11694, 26451, 15485, 2988, 250, 16, 1, 1, 1, 1, 42, 6006
Offset: 1

Views

Author

R. H. Hardin Aug 23 2012

Keywords

Comments

Table starts
.1.1.1..1....1......1........1..........1...........1...........1...........1
.1.1.1..1....2......2........5..........5..........14..........14..........42
.1.1.1..2....5.....12.......42........110.........462........1274........6006
.1.1.1..2...10.....29......262........932.......11694.......46988......727846
.1.1.1..4...25....189.....2465......26451......530429.....7027942...187205626
.1.1.1..4...50....458....15485.....234217....14296434...297246092.26970790176
.1.1.1..8..125...2988...146205....6812794...673507749.48337803306
.1.1.1..8..250...7241...918637...60485308.18255280444
.1.1.1.16..625..47241..8674386.1761748159
.1.1.1.16.1250.114482.54503318
.1.1.1.32.3125.746892
.1.1.1.32.6250

Examples

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

Links

Crossrefs

Column 5 is A026383(n-1)
Row 2 is A000108(floor((n-1)/2))
Odd squares: A215870

Formula

Empirical for column k:
k=4: a(n) = 2*a(n-2)
k=5: a(n) = 5*a(n-2)
k=6: a(n) = 16*a(n-2) -3*a(n-4)
k=7: a(n) = 61*a(n-2) -99*a(n-4) -2*a(n-6)
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)

A215866 Number of permutations of 0..floor((n*6-2)/2) on odd squares of an n X 6 array such that each row, column, diagonal and (downwards) antidiagonal of odd squares is increasing.

Original entry on oeis.org

1, 5, 12, 78, 189, 1233, 2988, 19494, 47241, 308205, 746892, 4872798, 11808549, 77040153, 186696108, 1218024054, 2951712081, 19257264405, 46667304972, 304462158318, 737821743309, 4813622739873, 11665145978028, 76104577363014
Offset: 1

Views

Author

R. H. Hardin, Aug 25 2012

Keywords

Comments

Column 6 of A215870.

Examples

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

Links

Formula

Empirical: a(n) = 16*a(n-2) -3*a(n-4).
Empirical: g.f.: -x*(x-1)*(2*x^2+6*x+1) / ( 1-16*x^2+3*x^4 ). - R. J. Mathar, Nov 27 2015

A215867 Number of permutations of 0..floor((n*7-2)/2) on odd squares of an n X 7 array such that each row, column, diagonal and (downwards) antidiagonal of odd squares is increasing.

Original entry on oeis.org

1, 5, 29, 262, 1642, 15485, 97289, 918637, 5772013, 54503318, 342457898, 3233726365, 20318307913, 191859642509, 1205501906765, 11383190276278, 71523418913482, 675374034791837, 4243543228336841, 40070496565665517
Offset: 1

Views

Author

R. H. Hardin, Aug 25 2012

Keywords

Comments

Column 7 of A215870.

Examples

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

Links

Formula

Empirical: a(n) = 61*a(n-2) -99*a(n-4) -2*a(n-6).
Empirical: g.f.: -x*(-1 -5*x +32*x^2 +43*x^3 +28*x^4 +2*x^5) / ( 1 -61*x^2 +99*x^4 +2*x^6 ). - R. J. Mathar, Nov 27 2015

A215868 Number of permutations of 0..floor((n*8-2)/2) on odd squares of an nX8 array such that each row, column, diagonal and (downwards) antidiagonal of odd squares is increasing.

Original entry on oeis.org

1, 14, 110, 3001, 26451, 767560, 6812794, 198409297, 1761748159, 51317680568, 455678075546, 13273519382093, 117863060852067, 3433253982499552, 30485799411892266, 888026282079787049, 7885286478349158743
Offset: 1

Views

Author

R. H. Hardin Aug 25 2012

Keywords

Comments

Column 8 of A215870

Examples

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

Links

Formula

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

A215869 Number of permutations of 0..floor((n*9-2)/2) on odd squares of an nX9 array such that each row, column, diagonal and (downwards) antidiagonal of odd squares is increasing.

Original entry on oeis.org

1, 14, 290, 11694, 307874, 14296434, 386699176, 18255280444, 494952307400, 23397688110992, 634501639410480, 29997930933948284, 813501010455768664, 38461009542931961924, 1043008988814913191696, 49311812528326463481148
Offset: 1

Views

Author

R. H. Hardin Aug 25 2012

Keywords

Comments

Column 9 of A215870

Examples

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

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)

A215871 Number of permutations of 0..floor((3*n-2)/2) on odd squares of an 3Xn array such that each row, column, diagonal and (downwards) antidiagonal of odd squares is increasing.

Original entry on oeis.org

1, 1, 1, 2, 4, 12, 29, 110, 290, 1274, 3532, 17136, 49100, 255816, 750325, 4124406, 12310294, 70549050, 213446666, 1264752060, 3868253164, 23555382240, 72686739116, 452806924752
Offset: 1

Views

Author

R. H. Hardin Aug 25 2012

Keywords

Comments

Row 3 of A215870

Examples

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

A215872 Number of permutations of 0..floor((4*n-2)/2) on odd squares of an 4Xn array such that each row, column, diagonal and (downwards) antidiagonal of odd squares is increasing.

Original entry on oeis.org

1, 1, 1, 4, 10, 78, 262, 3001, 11694, 170594, 727846, 12517074, 56797272, 1100044792, 5219906670, 110598847073, 542976951374, 12341741030502
Offset: 1

Views

Author

R. H. Hardin Aug 25 2012

Keywords

Comments

Row 4 of A215870

Examples

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

A215873 Number of permutations of 0..floor((5*n-2)/2) on odd squares of an 5Xn array such that each row, column, diagonal and (downwards) antidiagonal of odd squares is increasing.

Original entry on oeis.org

1, 1, 1, 4, 20, 189, 1642, 26451, 307874, 7027942, 98057806, 2850280812, 44974137856
Offset: 1

Views

Author

R. H. Hardin Aug 25 2012

Keywords

Comments

Row 5 of A215870

Examples

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

A215874 Number of permutations of 0..floor((6*n-2)/2) on odd squares of an 6Xn array such that each row, column, diagonal and (downwards) antidiagonal of odd squares is increasing.

Original entry on oeis.org

1, 1, 1, 8, 50, 1233, 15485, 767560, 14296434, 1124811332
Offset: 1

Views

Author

R. H. Hardin Aug 25 2012

Keywords

Comments

Row 6 of A215870

Examples

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

A215875 Number of permutations of 0..floor((7*n-2)/2) on odd squares of an 7Xn array such that each row, column, diagonal and (downwards) antidiagonal of odd squares is increasing.

Original entry on oeis.org

1, 1, 1, 8, 100, 2988, 97289, 6812794, 386699176, 48337803306
Offset: 1

Views

Author

R. H. Hardin Aug 25 2012

Keywords

Comments

Row 7 of A215870

Examples

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

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