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.

A268051 Number of n X n 0..2 arrays with new values introduced in each row and column in sequential order starting with zero.

Original entry on oeis.org

1, 2, 18, 1082, 560778, 2666449962, 116124404018058, 45944873892068760842, 164311405786753523443114218, 5298327789094557001583255058644522, 1538780360110790603716817054271433490324298
Offset: 1

Views

Author

R. H. Hardin, Jan 25 2016

Keywords

Comments

Diagonal of A268056.

Examples

			Some solutions for n=4
..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
..0..1..0..1....0..0..0..0....0..1..1..0....0..0..1..1....0..1..1..0
..0..0..1..0....0..1..1..0....0..1..1..0....0..0..1..1....0..1..2..0
..0..1..0..2....0..0..0..0....0..1..0..1....0..0..1..2....0..1..1..0

Links

Crossrefs

Cf. A268056.

A268052 Number of n X 4 0..2 arrays with new values introduced in each row and column in sequential order starting with zero.

Original entry on oeis.org

1, 8, 86, 1082, 14554, 200818, 2796826, 39082562, 546791114, 7653252338, 107136417466, 1499864270242, 20997871916074, 293969067496658, 4115561248327706, 57617828993493122, 806649463493495434
Offset: 1

Views

Author

R. H. Hardin, Jan 25 2016

Keywords

Examples

			Some solutions for n=4:
..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
..0..1..0..1....0..1..1..0....0..0..1..1....0..1..1..1....0..1..0..1
..0..0..1..1....0..1..2..1....0..0..0..0....0..1..1..2....0..0..1..2
..0..1..0..0....0..1..0..1....0..1..1..0....0..1..0..1....0..1..1..1

Links

Crossrefs

Column 4 of A268056.

Formula

Empirical: a(n) = 21*a(n-1) - 108*a(n-2) + 140*a(n-3).
Conjectures from Colin Barker, Jan 11 2019: (Start)
G.f.: x*(1 - 13*x + 26*x^2) / ((1 - 2*x)*(1 - 5*x)*(1 - 14*x)).
a(n) = (105*2^n + 196*5^n + 25*2^(1+n)*7^n) / 1890.
(End)

A268053 Number of n X 5 0..2 arrays with new values introduced in each row and column in sequential order starting with zero.

Original entry on oeis.org

1, 16, 422, 14554, 560778, 22501266, 915745002, 37450557314, 1534144563898, 62881338826706, 2577874694337482, 105689219894749474, 4333207020625065818, 177660773919610165746, 7284081735763859949162, 298647211237276504916034
Offset: 1

Views

Author

R. H. Hardin, Jan 25 2016

Keywords

Examples

			Some solutions for n=4:
..0..0..0..0..0....0..0..0..0..0....0..0..0..0..0....0..0..0..0..0
..0..1..1..1..0....0..0..0..1..1....0..1..1..0..1....0..1..1..0..1
..0..0..0..1..0....0..0..1..2..0....0..0..0..0..1....0..0..0..1..2
..0..1..0..2..0....0..1..2..0..2....0..1..2..0..0....0..0..1..2..2

Links

Crossrefs

Column 5 of A268056.

Formula

Empirical: a(n) = 62*a(n-1) - 969*a(n-2) + 4568*a(n-3) - 5740*a(n-4).
Conjectures from Colin Barker, Jan 11 2019: (Start)
G.f.: x*(1 - 46*x + 399*x^2 - 674*x^3) / ((1 - 2*x)*(1 - 5*x)*(1 - 14*x)*(1 - 41*x)).
a(n) = (38745*2^n + 127428*5^n + 17425*2^(2+n)*7^n + 9800*41^n) / 2092230.
(End)

A268054 Number of n X 6 0..2 arrays with new values introduced in each row and column in sequential order starting with zero.

Original entry on oeis.org

1, 32, 2094, 200818, 22501266, 2666449962, 322124540754, 39169337042938, 4773343640706306, 582130110629340842, 71010944836457411314, 8662969218697854336858, 1056867236907904064782946
Offset: 1

Views

Author

R. H. Hardin, Jan 25 2016

Keywords

Examples

			Some solutions for n=3:
..0..0..0..0..0..0....0..0..0..0..0..0....0..0..0..0..0..0....0..0..0..0..0..0
..0..1..0..1..0..0....0..1..1..1..1..1....0..1..0..1..0..0....0..1..0..0..0..1
..0..0..1..2..1..1....0..0..1..2..2..1....0..0..0..0..0..1....0..1..1..1..0..2

Links

Crossrefs

Column 6 of A268056.

Formula

Empirical: a(n) = 184*a(n-1) - 8533*a(n-2) + 122786*a(n-3) - 563036*a(n-4) + 700280*a(n-5).
Empirical g.f.: x*(1 - 152*x + 4739*x^2 - 34208*x^3 + 52740*x^4) / ((1 - 2*x)*(1 - 5*x)*(1 - 14*x)*(1 - 41*x)*(1 - 122*x)). - Colin Barker, Jan 11 2019

A268055 Number of nX7 0..2 arrays with new values introduced in each row and column in sequential order starting with zero.

Original entry on oeis.org

1, 64, 10438, 2796826, 915745002, 322124540754, 116124404018058, 42209510913723266, 15385058360607977882, 5612935794998414602514, 2048403161005485984441578, 747628311641175955079078306
Offset: 1

Views

Author

R. H. Hardin, Jan 25 2016

Keywords

Comments

Column 7 of A268056.

Examples

			Some solutions for n=3
..0..0..0..0..0..0..0....0..0..0..0..0..0..0....0..0..0..0..0..0..0
..0..1..0..1..0..1..1....0..1..1..1..0..1..1....0..1..1..1..1..0..1
..0..1..0..2..0..0..2....0..1..0..2..1..0..2....0..1..2..1..1..1..0

Links

Crossrefs

Cf. A268056.

Formula

Empirical: a(n) = 549*a(n-1) -75693*a(n-2) +3237331*a(n-3) -45379926*a(n-4) +206208420*a(n-5) -255602200*a(n-6)
Showing 1-5 of 5 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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