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 11 results. Next

A221618 Number of n X n arrays with each row a permutation of 1..n having at least as many downsteps as the preceding row.

Original entry on oeis.org

1, 3, 112, 85035, 3451956516, 7575106427737240, 2031241364747667201263520, 57096186419355436503540544000542003, 350680349722258761627197454626353435730368352560
Offset: 1

Views

Author

R. H. Hardin Jan 21 2013

Keywords

Comments

Diagonal of A221623

Examples

			Some solutions for n=3
..1..2..3....1..2..3....3..1..2....3..1..2....2..1..3....1..2..3....2..3..1
..2..1..3....3..1..2....3..1..2....2..3..1....1..3..2....1..3..2....3..1..2
..3..2..1....3..2..1....2..3..1....3..1..2....2..3..1....3..2..1....3..1..2

Links

A221619 Number of n X 4 arrays with each row a permutation of 1..4 having at least as many downsteps as the preceding row.

Original entry on oeis.org

24, 410, 6120, 85035, 1130256, 14576404, 183919920, 2282493365, 27960543720, 338950264686, 4073680032984, 48607978698655, 576460247379360, 6800560019808680, 79860630502888416, 934066108666694889
Offset: 1

Views

Author

R. H. Hardin, Jan 21 2013

Keywords

Comments

Column 4 of A221623.

Examples

			Some solutions for n=3:
..2..4..1..3....2..1..3..4....3..4..1..2....3..4..2..1....2..1..4..3
..3..2..1..4....2..4..1..3....1..2..4..3....4..1..3..2....3..2..4..1
..4..3..1..2....3..1..2..4....2..4..3..1....4..3..2..1....1..4..3..2

Links

Crossrefs

Cf. A221623.

Formula

Empirical: a(n) = 24*a(n-1) - 166*a(n-2) + 264*a(n-3) - 121*a(n-4).
Conjectures from Colin Barker, Aug 09 2018: (Start)
G.f.: x*(12 - 11*x)*(2 - 12*x + 11*x^2) / ((1 - x)^2*(1 - 11*x)^2).
a(n) = (4*(4+11^(2+n)) + 5*(1+11^(2+n))*n) / 500.
(End)

A221620 Number of n X 5 arrays with each row a permutation of 1..5 having at least as many downsteps as the preceding row.

Original entry on oeis.org

120, 10055, 738150, 51149685, 3451956516, 230141263315, 15258126049410, 1009051056050225, 66655625407012320, 4400938611593606031, 290509268912775739710, 19174945298440265379565, 1265583745617128902739100
Offset: 1

Views

Author

R. H. Hardin, Jan 21 2013

Keywords

Comments

Column 5 of A221623.

Examples

			Some solutions for n=3:
..1..2..3..4..5....1..2..4..3..5....1..2..4..3..5....1..2..3..5..4
..4..5..1..3..2....1..2..5..4..3....4..3..1..2..5....1..2..5..3..4
..5..1..2..4..3....3..5..4..1..2....5..3..4..1..2....1..3..4..5..2

Links

Crossrefs

Cf. A221623.

Formula

Empirical: a(n) = 120*a(n-1) - 4345*a(n-2) + 52950*a(n-3) - 93340*a(n-4) + 44616*a(n-5).
Empirical g.f.: x*(120 - 4345*x + 52950*x^2 - 93340*x^3 + 44616*x^4) / ((1 - x)^2*(1 - 26*x)^2*(1 - 66*x)). - Colin Barker, Aug 09 2018

A221621 Number of nX6 arrays with each row a permutation of 1..6 having at least as many downsteps as the preceding row.

Original entry on oeis.org

720, 353654, 148700748, 57614883627, 21241004664348, 7575106427737240, 2638115823321645192, 902542985526634773509, 304529313276100670030616, 101620178879261858322711162, 33604296810830843896378600020
Offset: 1

Views

Author

R. H. Hardin Jan 21 2013

Keywords

Comments

Column 6 of A221623

Examples

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

Links

Formula

Empirical: a(n) = 720*a(n-1) -164746*a(n-2) +12686988*a(n-3) -321204409*a(n-4) +605003244*a(n-5) -296321796*a(n-6)

A221622 Number of nX7 arrays with each row a permutation of 1..7 having at least as many downsteps as the preceding row.

Original entry on oeis.org

5040, 17052210, 49096652080, 130516916069715, 332469512259607296, 827196295133181978340, 2031241364747667201263520, 4951481629224145844957738085, 12021159412525485182456506260880
Offset: 1

Views

Author

R. H. Hardin Jan 21 2013

Keywords

Comments

Column 7 of A221623

Examples

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

Links

Formula

Empirical: a(n) = 5040*a(n-1) -8349390*a(n-2) +5234439280*a(n-3) -936232732785*a(n-4) +51206316902496*a(n-5) -99624831647040*a(n-6) +49349521382400*a(n-7)

A221624 Number of 2Xn arrays with each row a permutation of 1..n having at least as many downsteps as the preceding row.

Original entry on oeis.org

1, 3, 27, 410, 10055, 353654, 17052210, 1075295220, 86037489675, 8510611773950, 1020010974544958, 145633667181394028, 24424236713657975558, 4754016566455947216412, 1062903928921857001102308
Offset: 1

Views

Author

R. H. Hardin Jan 21 2013

Keywords

Comments

Row 2 of A221623

Examples

			Some solutions for n=3
..2..3..1....2..3..1....2..1..3....3..1..2....2..1..3....1..3..2....1..2..3
..3..2..1....1..3..2....2..3..1....2..1..3....2..1..3....2..3..1....1..2..3

Links

A221625 Number of 3Xn arrays with each row a permutation of 1..n having at least as many downsteps as the preceding row.

Original entry on oeis.org

1, 4, 112, 6120, 738150, 148700748, 49096652080, 24099422236160, 17023170538890750, 16517958827528755300, 21433818529290626472948, 36180795747764068402865136, 77856103174007703918070147632
Offset: 1

Views

Author

R. H. Hardin Jan 21 2013

Keywords

Comments

Row 3 of A221623

Examples

			Some solutions for n=3
..3..1..2....1..2..3....1..3..2....1..2..3....1..2..3....2..3..1....2..3..1
..1..3..2....3..1..2....3..1..2....1..2..3....2..1..3....2..3..1....1..3..2
..1..3..2....2..3..1....3..2..1....1..2..3....3..2..1....2..1..3....3..1..2

Links

A221626 Number of 4Xn arrays with each row a permutation of 1..n having at least as many downsteps as the preceding row.

Original entry on oeis.org

1, 5, 453, 85035, 51149685, 57614883627, 130516916069715, 492362067027383802, 3063154239917651379537, 28932140956374841410316707, 405028623674958829496315433651, 8040080740216333451541433497055002
Offset: 1

Views

Author

R. H. Hardin Jan 21 2013

Keywords

Comments

Row 4 of A221623

Examples

			Some solutions for n=3
..2..3..1....1..3..2....1..2..3....2..3..1....2..1..3....1..2..3....2..3..1
..2..3..1....2..1..3....1..2..3....1..3..2....3..1..2....1..2..3....2..3..1
..2..3..1....2..3..1....3..1..2....2..1..3....3..1..2....1..3..2....3..1..2
..1..3..2....2..3..1....2..1..3....3..1..2....2..3..1....2..1..3....1..3..2

Links

A221627 Number of 5Xn arrays with each row a permutation of 1..n having at least as many downsteps as the preceding row.

Original entry on oeis.org

1, 6, 1818, 1130256, 3451956516, 21241004664348, 332469512259607296, 9510929074212911717760, 521875340203828179569609700, 47602100904962622927705491352020, 7181861163349151796773697873026037828
Offset: 1

Views

Author

R. H. Hardin Jan 21 2013

Keywords

Comments

Row 5 of A221623

Examples

			Some solutions for n=3
..1..3..2....1..3..2....2..3..1....3..1..2....2..1..3....1..3..2....3..1..2
..1..3..2....1..3..2....1..3..2....2..3..1....2..1..3....3..1..2....2..1..3
..2..1..3....2..1..3....1..3..2....3..1..2....2..1..3....2..1..3....3..1..2
..2..1..3....1..3..2....2..3..1....2..1..3....3..2..1....1..3..2....2..3..1
..2..3..1....2..3..1....1..3..2....1..3..2....3..2..1....3..2..1....3..1..2

Links

A221628 Number of 6Xn arrays with each row a permutation of 1..n having at least as many downsteps as the preceding row.

Original entry on oeis.org

1, 7, 7279, 14576404, 230141263315, 7575106427737240, 827196295133181978340, 177037611175595181692394660, 86030164534670200470739520304375, 75149351745335662460465241596540458600
Offset: 1

Views

Author

R. H. Hardin Jan 21 2013

Keywords

Comments

Row 6 of A221623

Examples

			Some solutions for n=3
..2..3..1....1..2..3....1..3..2....1..3..2....3..1..2....1..3..2....3..1..2
..1..3..2....1..2..3....2..1..3....1..3..2....3..1..2....2..3..1....1..3..2
..3..1..2....2..1..3....2..3..1....2..3..1....1..3..2....2..1..3....2..1..3
..1..3..2....2..3..1....2..1..3....2..3..1....1..3..2....3..1..2....2..1..3
..2..3..1....3..1..2....1..3..2....3..1..2....2..1..3....2..3..1....2..1..3
..3..1..2....2..3..1....2..3..1....2..3..1....2..3..1....1..3..2....3..2..1

Links

Showing 1-10 of 11 results. Next

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