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 1-6 of 6 results.

A252998 Number of n X n nonnegative integer arrays with upper left 0 and lower right its king-move distance away minus 3 and every value within 3 of its king move distance from the upper left and every value increasing by 0 or 1 with every step right, diagonally se or down.

Original entry on oeis.org

0, 0, 0, 1, 69, 3072, 122833, 4915726, 204051186, 8849413857, 399736867216, 18698541563923, 900653139548828, 44458651801451163, 2240500172425946056, 114922424191743943701, 5985232324581998309113, 315879022416448194306768
Offset: 1

Views

Author

R. H. Hardin, Dec 25 2014

Keywords

Comments

Diagonal of A253004.

Examples

			Some solutions for n=6:
..0..0..1..1..1..2....0..0..1..1..1..2....0..1..1..1..2..2....0..0..1..1..1..2
..0..0..1..1..1..2....0..1..1..1..2..2....1..1..1..1..2..2....0..1..1..1..1..2
..1..1..1..1..1..2....0..1..1..2..2..2....1..1..1..2..2..2....0..1..1..2..2..2
..1..1..2..2..2..2....1..1..1..2..2..2....2..2..2..2..2..2....1..1..1..2..2..2
..1..2..2..2..2..2....1..1..1..2..2..2....2..2..2..2..2..2....1..2..2..2..2..2
..2..2..2..2..2..2....2..2..2..2..2..2....2..2..2..2..2..2....2..2..2..2..2..2

Links

Crossrefs

Cf. A253004.

A252999 Number of n X 3 nonnegative integer arrays with upper left 0 and lower right its king-move distance away minus 3 and every value within 3 of its king move distance from the upper left and every value increasing by 0 or 1 with every step right, diagonally se or down.

Original entry on oeis.org

0, 0, 0, 1, 34, 279, 1028, 2601, 5318, 9499, 15464, 23533, 34026, 47263, 63564, 83249, 106638, 134051, 165808, 202229, 243634, 290343, 342676, 400953, 465494, 536619, 614648, 699901, 792698, 893359, 1002204, 1119553, 1245726, 1381043, 1525824
Offset: 1

Views

Author

R. H. Hardin, Dec 25 2014

Keywords

Examples

			Some solutions for n=6:
..0..0..0....0..1..1....0..1..2....0..0..1....0..0..1....0..0..1....0..1..1
..0..0..1....1..1..2....1..1..2....0..1..1....0..1..1....1..1..1....1..1..2
..0..0..1....1..2..2....1..1..2....0..1..2....1..1..1....1..1..1....1..1..2
..1..1..1....2..2..2....1..2..2....1..1..2....1..1..2....1..1..2....1..1..2
..1..1..2....2..2..2....1..2..2....1..2..2....2..2..2....1..2..2....1..2..2
..2..2..2....2..2..2....2..2..2....2..2..2....2..2..2....2..2..2....2..2..2

Links

Crossrefs

Column 3 of A253004.

Formula

Empirical: a(n) = (160/3)*n^3 - 708*n^2 + (9539/3)*n - 4831 for n>4.
Conjectures from Colin Barker, Dec 08 2018: (Start)
G.f.: x^4*(1 + 30*x + 149*x^2 + 112*x^3 + 28*x^4) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>8.
(End)

A253000 Number of n X 4 nonnegative integer arrays with upper left 0 and lower right its king-move distance away minus 3 and every value within 3 of its king move distance from the upper left and every value increasing by 0 or 1 with every step right, diagonally se or down.

Original entry on oeis.org

1, 1, 1, 1, 69, 1132, 7235, 25233, 63135, 129133, 231419, 378185, 577623, 837925, 1167283, 1573889, 2065935, 2651613, 3339115, 4136633, 5052359, 6094485, 7271203, 8590705, 10061183, 11690829, 13487835, 15460393, 17616695, 19964933, 22513299
Offset: 1

Views

Author

R. H. Hardin, Dec 25 2014

Keywords

Examples

			Some solutions for n=6:
..0..0..0..0....0..0..0..0....0..0..0..0....0..1..1..1....0..1..1..2
..0..0..0..1....1..1..1..1....0..1..1..1....0..1..1..1....1..1..1..2
..0..1..1..1....1..1..2..2....1..1..1..2....1..1..2..2....1..1..1..2
..0..1..2..2....1..1..2..2....2..2..2..2....1..2..2..2....1..1..1..2
..1..1..2..2....1..2..2..2....2..2..2..2....1..2..2..2....1..1..1..2
..2..2..2..2....2..2..2..2....2..2..2..2....2..2..2..2....2..2..2..2

Links

Crossrefs

Column 4 of A253004.

Formula

Empirical: a(n) = (4096/3)*n^3 - 22816*n^2 + (388490/3)*n - 249567 for n>6.
Conjectures from Colin Barker, Dec 08 2018: (Start)
G.f.: x*(1 - 3*x + 3*x^2 - x^3 + 68*x^4 + 859*x^5 + 3118*x^6 + 2810*x^7 + 1154*x^8 + 183*x^9) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>10.
(End)

A253001 Number of n X 5 nonnegative integer arrays with upper left 0 and lower right its king-move distance away minus 3 and every value within 3 of its king move distance from the upper left and every value increasing by 0 or 1 with every step right, diagonally se or down.

Original entry on oeis.org

4, 14, 34, 69, 69, 3072, 39758, 228484, 775433, 1932763, 3965261, 7139167, 11720721, 17976163, 26171733, 36573671, 49448217, 65061611, 83680093, 105569903, 130997281, 160228467, 193529701, 231167223, 273407273, 320516091, 372759917
Offset: 1

Views

Author

R. H. Hardin, Dec 25 2014

Keywords

Examples

			Some solutions for n=6:
..0..0..0..1..2....0..0..0..1..2....0..0..0..0..1....0..0..1..1..1
..1..1..1..1..2....0..1..1..1..2....0..0..1..1..1....0..0..1..1..1
..1..1..2..2..2....1..1..1..1..2....0..1..1..1..1....1..1..1..2..2
..1..2..2..2..2....1..1..1..1..2....1..1..1..1..2....1..1..1..2..2
..1..2..2..2..2....2..2..2..2..2....1..1..1..2..2....2..2..2..2..2
..2..2..2..2..2....2..2..2..2..2....2..2..2..2..2....2..2..2..2..2

Links

Crossrefs

Column 5 of A253004.

Formula

Empirical: a(n) = (133120/3)*n^3 - 893616*n^2 + (18332582/3)*n - 14187577 for n>8.
Conjectures from Colin Barker, Dec 08 2018: (Start)
G.f.: x*(4 - 2*x + 2*x^2 + x^3 - 55*x^4 + 3088*x^5 + 27642*x^6 + 87677*x^7 + 87826*x^8 + 45975*x^9 + 12629*x^10 + 1453*x^11) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>12.
(End)

A253002 Number of nX6 nonnegative integer arrays with upper left 0 and lower right its king-move distance away minus 3 and every value within 3 of its king move distance from the upper left and every value increasing by 0 or 1 with every step right, diagonally se or down.

Original entry on oeis.org

10, 55, 279, 1132, 3072, 3072, 122833, 1486152, 8270017, 27983105, 70187099, 145197755, 263486747, 435539835, 671842779, 982881339, 1379141275, 1871108347, 2469268315, 3184106939, 4026109979, 5005763195, 6133552347, 7419963195
Offset: 1

Views

Author

R. H. Hardin, Dec 25 2014

Keywords

Comments

Column 6 of A253004

Examples

			Some solutions for n=6
..0..0..1..1..1..2....0..0..0..1..1..2....0..0..0..1..1..2....0..0..0..0..1..2
..0..0..1..1..2..2....0..0..0..1..1..2....1..1..1..1..2..2....0..0..0..0..1..2
..0..1..1..2..2..2....0..1..1..1..1..2....1..1..2..2..2..2....1..1..1..1..1..2
..1..1..2..2..2..2....0..1..1..1..1..2....1..2..2..2..2..2....1..1..1..1..1..2
..1..2..2..2..2..2....1..1..1..1..2..2....2..2..2..2..2..2....2..2..2..2..2..2
..2..2..2..2..2..2....2..2..2..2..2..2....2..2..2..2..2..2....2..2..2..2..2..2

Links

Formula

Empirical: a(n) = (5242880/3)*n^3 - 41275392*n^2 + (991610656/3)*n - 897487301 for n>10

A253003 Number of nX7 nonnegative integer arrays with upper left 0 and lower right its king-move distance away minus 3 and every value within 3 of its king move distance from the upper left and every value increasing by 0 or 1 with every step right, diagonally se or down.

Original entry on oeis.org

20, 140, 1028, 7235, 39758, 122833, 122833, 4915726, 59154789, 329035981, 1124010769, 2853903059, 5973571711, 10950733467, 18255251895, 28357151187, 41726455535, 58833189131, 80147376167, 106139040835, 137278207327
Offset: 1

Views

Author

R. H. Hardin, Dec 25 2014

Keywords

Comments

Column 7 of A253004

Examples

			Some solutions for n=6
..0..1..1..1..1..2..3....0..0..1..1..1..2..3....0..1..1..1..2..3..3
..1..1..1..1..2..2..3....0..0..1..1..2..2..3....0..1..2..2..2..3..3
..1..1..1..1..2..2..3....0..1..1..1..2..2..3....1..1..2..2..2..3..3
..1..1..2..2..2..3..3....0..1..1..2..2..3..3....1..1..2..2..3..3..3
..1..2..2..2..3..3..3....1..1..1..2..3..3..3....2..2..2..3..3..3..3
..2..2..2..3..3..3..3....2..2..2..2..3..3..3....2..2..3..3..3..3..3

Links

Formula

Empirical: a(n) = (235012096/3)*n^3 - 2126491008*n^2 + (58625640404/3)*n - 60801081325 for n>12
Showing 1-6 of 6 results.

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