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.

A252830 Number of n X n nonnegative integer arrays with upper left 0 and every value within 2 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, 5, 44, 493, 6068, 78674, 1056756, 14564701, 204666202, 2919462498, 42143180174, 614251526864, 9024782449736, 133489812361806, 1985873221687284, 29689739907869581, 445797648515664064, 6719243690952576928
Offset: 1

Views

Author

R. H. Hardin, Dec 22 2014

Keywords

Comments

Diagonal of A252836

Examples

			Some solutions for n=4
..0..0..1..2....0..0..1..1....0..0..1..1....0..0..1..1....0..0..0..1
..1..1..1..2....1..1..1..1....1..1..1..2....1..1..1..1....1..1..1..1
..1..1..2..2....1..1..1..1....1..1..1..2....1..2..2..2....1..1..1..1
..2..2..2..2....2..2..2..2....1..2..2..2....1..2..2..3....2..2..2..2

Links

A252831 Number of n X 3 nonnegative integer arrays with upper left 0 and every value within 2 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, 13, 44, 127, 288, 529, 850, 1251, 1732, 2293, 2934, 3655, 4456, 5337, 6298, 7339, 8460, 9661, 10942, 12303, 13744, 15265, 16866, 18547, 20308, 22149, 24070, 26071, 28152, 30313, 32554, 34875, 37276, 39757, 42318, 44959, 47680, 50481, 53362, 56323
Offset: 1

Views

Author

R. H. Hardin, Dec 22 2014

Keywords

Examples

			Some solutions for n=4:
..0..1..2....0..0..0....0..1..1....0..1..1....0..1..2....0..0..1....0..0..0
..0..1..2....0..0..1....1..1..2....1..1..1....1..1..2....1..1..1....0..0..1
..1..1..2....1..1..1....1..1..2....1..2..2....2..2..2....1..1..2....0..1..1
..2..2..2....2..2..2....1..2..2....1..2..3....3..3..3....1..1..2....1..1..2

Links

Crossrefs

Column 3 of A252836.

Formula

Empirical: a(n) = 40*n^2 - 199*n + 283 for n>3.
Conjectures from Colin Barker, Dec 06 2018: (Start)
G.f.: x*(4 + x + 17*x^2 + 30*x^3 + 26*x^4 + 2*x^5) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>6.
(End)

A252832 Number of n X 4 nonnegative integer arrays with upper left 0 and every value within 2 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

7, 29, 127, 493, 1474, 3365, 6211, 10017, 14783, 20509, 27195, 34841, 43447, 53013, 63539, 75025, 87471, 100877, 115243, 130569, 146855, 164101, 182307, 201473, 221599, 242685, 264731, 287737, 311703, 336629, 362515, 389361, 417167, 445933
Offset: 1

Views

Author

R. H. Hardin, Dec 22 2014

Keywords

Examples

			Some solutions for n=4:
..0..1..1..1....0..0..1..1....0..1..1..2....0..0..1..1....0..1..1..1
..0..1..1..1....1..1..1..1....0..1..1..2....0..0..1..1....1..1..2..2
..0..1..1..2....1..2..2..2....0..1..1..2....0..1..1..2....1..2..2..2
..1..1..2..2....1..2..2..3....1..1..2..2....1..1..1..2....2..2..3..3

Links

Crossrefs

Column 4 of A252836.

Formula

Empirical: a(n) = 480*n^2 - 3394*n + 6449 for n>5.
Conjectures from Colin Barker, Dec 06 2018: (Start)
G.f.: x*(7 + 8*x + 61*x^2 + 192*x^3 + 347*x^4 + 295*x^5 + 45*x^6 + 5*x^7) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>8.
(End)

A252833 Number of n X 5 nonnegative integer arrays with upper left 0 and every value within 2 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

11, 53, 288, 1474, 6068, 18528, 42738, 79563, 129173, 191583, 266793, 354803, 455613, 569223, 695633, 834843, 986853, 1151663, 1329273, 1519683, 1722893, 1938903, 2167713, 2409323, 2663733, 2930943, 3210953, 3503763, 3809373, 4127783
Offset: 1

Views

Author

R. H. Hardin, Dec 22 2014

Keywords

Examples

			Some solutions for n=4:
..0..1..1..2..2....0..1..1..2..3....0..0..1..2..3....0..1..1..2..2
..0..1..1..2..3....1..1..1..2..3....1..1..1..2..3....1..1..1..2..3
..1..1..2..2..3....2..2..2..2..3....1..2..2..2..3....1..1..2..2..3
..1..2..2..2..3....2..3..3..3..3....1..2..2..3..3....2..2..2..3..3

Links

Crossrefs

Column 5 of A252836.

Formula

Empirical: a(n) = 6400*n^2 - 59190*n + 143483 for n>7.
Conjectures from Colin Barker, Dec 06 2018: (Start)
G.f.: x*(11 + 20*x + 162*x^2 + 758*x^3 + 2457*x^4 + 4458*x^5 + 3884*x^6 + 865*x^7+ 170*x^8 + 15*x^9) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>10.
(End)

A252834 Number of n X 6 nonnegative integer arrays with upper left 0 and every value within 2 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

16, 85, 529, 3365, 18528, 78674, 244131, 569420, 1070036, 1750150, 2610438, 3650950, 4871686, 6272646, 7853830, 9615238, 11556870, 13678726, 15980806, 18463110, 21125638, 23968390, 26991366, 30194566, 33577990, 37141638, 40885510
Offset: 1

Views

Author

R. H. Hardin, Dec 22 2014

Keywords

Examples

			Some solutions for n=4:
..0..0..1..1..2..3....0..1..2..2..3..4....0..1..2..3..3..3....0..1..2..2..3..4
..0..1..1..2..2..3....1..1..2..3..3..4....1..1..2..3..3..3....1..1..2..2..3..4
..1..1..1..2..2..3....1..1..2..3..3..4....1..2..2..3..3..3....1..2..2..3..3..4
..1..1..1..2..2..3....1..2..2..3..4..4....2..2..3..3..3..4....1..2..3..3..3..4

Links

Crossrefs

Column 6 of A252836.

Formula

Empirical: a(n) = 90112*n^2 - 1032064*n + 3059590 for n>9.
Conjectures from Colin Barker, Dec 07 2018: (Start)
G.f.: x*(16 + 37*x + 322*x^2 + 2017*x^3 + 9935*x^4 + 32656*x^5 + 60328*x^6 + 54521*x^7 + 15495*x^8 + 4171*x^9 + 676*x^10 + 50*x^11) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>12.
(End)

A252835 Number of nX7 nonnegative integer arrays with upper left 0 and every value within 2 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

22, 125, 850, 6211, 42738, 244131, 1056756, 3320837, 7822881, 14827629, 24422839, 36628371, 51446975, 68878827, 88923927, 111582275, 136853871, 164738715, 195236807, 228348147, 264072735, 302410571, 343361655, 386925987, 433103567
Offset: 1

Views

Author

R. H. Hardin, Dec 22 2014

Keywords

Comments

Column 7 of A252836

Examples

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

Links

Formula

Empirical: a(n) = 1306624*n^2 - 17846996*n + 62638467 for n>11
Showing 1-6 of 6 results.

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

Content is available under The OEIS End-User License Agreement.