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.

A253006 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 increasing by 0 or 1 with every step right, diagonally se or down.

Original entry on oeis.org

0, 0, 0, 1, 54, 632, 2902, 8416, 18770, 35564, 60398, 94872, 140586, 199140, 272134, 361168, 467842, 593756, 740510, 909704, 1102938, 1321812, 1567926, 1842880, 2148274, 2485708, 2856782, 3263096, 3706250, 4187844, 4709478, 5272752, 5879266
Offset: 1

Views

Author

R. H. Hardin, Dec 25 2014

Keywords

Examples

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

Links

Crossrefs

Column 3 of A253011.

Formula

Empirical: a(n) = (800/3)*n^3 - 3980*n^2 + (60442/3)*n - 34576 for n>6.
Conjectures from Colin Barker, Dec 08 2018: (Start)
G.f.: x^4*(1 + 50*x + 422*x^2 + 694*x^3 + 385*x^4 + 44*x^5 + 4*x^6) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>10.
(End)

A253007 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 increasing by 0 or 1 with every step right, diagonally se or down.

Original entry on oeis.org

1, 1, 1, 1, 124, 3423, 33533, 158877, 490403, 1156178, 2286874, 4013538, 6467242, 9779058, 14080058, 19501314, 26173898, 34228882, 43797338, 55010338, 67998954, 82894258, 99827322, 118929218, 140331018, 164163794, 190558618, 219646562
Offset: 1

Views

Author

R. H. Hardin, Dec 25 2014

Keywords

Examples

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

Links

Crossrefs

Column 4 of A253011.

Formula

Empirical: a(n) = (65536/3)*n^3 - 422912*n^2 + (8343128/3)*n - 6208382 for n>9.
Conjectures from Colin Barker, Dec 08 2018: (Start)
G.f.: x*(1 - 3*x + 3*x^2 - x^3 + 123*x^4 + 2930*x^5 + 20582*x^6 + 44788*x^7 + 42525*x^8 + 17119*x^9 + 2605*x^10 + 375*x^11 + 25*x^12) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>13.
(End)

A253008 Number of nX5 nonnegative integer arrays with upper left 0 and lower right its king-move distance away minus 3 and every value increasing by 0 or 1 with every step right, diagonally se or down.

Original entry on oeis.org

4, 19, 54, 124, 250, 14795, 309990, 2853292, 14125312, 46481352, 116171792, 240747928, 438003360, 725775144, 1121905200, 1644235704, 2310608832, 3138866760, 4146851664, 5352405720, 6773371104, 8427589992, 10332904560
Offset: 1

Views

Author

R. H. Hardin, Dec 25 2014

Keywords

Comments

Column 5 of A253011

Examples

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

Links

Formula

Empirical: a(n) = 2973696*n^3 - 70716096*n^2 + 570494664*n - 1560617160 for n>12

A253009 Number of nX6 nonnegative integer arrays with upper left 0 and lower right its king-move distance away minus 3 and every value increasing by 0 or 1 with every step right, diagonally se or down.

Original entry on oeis.org

10, 85, 632, 3423, 14795, 54219, 2327062, 43197859, 395069496, 2063349297, 7250116841, 19242081848, 41884052188, 79190458776, 135212633776, 214009464108, 319640931500, 456167117868, 627648109484, 838143992620
Offset: 1

Views

Author

R. H. Hardin, Dec 25 2014

Keywords

Comments

Column 6 of A253011

Examples

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

Links

Formula

Empirical: a(n) = (2030043136/3)*n^3 - 19063373824*n^2 + (545623168640/3)*n - 587442631380 for n>15

A253010 Number of nX7 nonnegative integer arrays with upper left 0 and lower right its king-move distance away minus 3 and every value increasing by 0 or 1 with every step right, diagonally se or down.

Original entry on oeis.org

20, 231, 2902, 33533, 309990, 2327062, 14697256, 541365583, 9617848524, 90094114144, 499454404412, 1875291094664, 5288570216780, 12109231279152, 23836473347284, 42007667355832, 68169527721372, 103870860371584
Offset: 1

Views

Author

R. H. Hardin, Dec 25 2014

Keywords

Comments

Column 7 of A253011

Examples

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

Links

Formula

Empirical: a(n) = (774604193792/3)*n^3 - 8398560300416*n^2 + (277091586550828/3)*n - 343375674454152 for n>18

A253005 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 increasing by 0 or 1 with every step right, diagonally se or down.

Original entry on oeis.org

0, 0, 0, 1, 250, 54219, 14697256, 5713126349, 3406380649146, 3235013673306411, 5006915703789559516, 12814921349279258614386, 54759970343589573849950696, 393147238947490609962950665584, 4762079888047633609309896734274288
Offset: 1

Views

Author

R. H. Hardin, Dec 25 2014

Keywords

Comments

Diagonal of A253011.

Examples

			Some solutions for n=6:
..0..0..0..0..0..0....0..0..0..0..0..0....0..1..1..1..1..2....0..0..1..1..1..2
..0..0..0..0..0..1....0..0..0..1..1..1....1..1..1..1..1..2....0..0..1..1..1..2
..0..0..1..1..1..1....0..0..0..1..1..1....1..1..1..1..1..2....0..1..1..1..2..2
..0..0..1..1..1..2....0..0..0..1..1..2....1..1..1..1..1..2....1..1..1..2..2..2
..0..0..1..1..1..2....0..0..0..1..1..2....1..1..1..1..1..2....1..1..1..2..2..2
..1..1..1..1..1..2....1..1..1..1..2..2....1..2..2..2..2..2....1..1..1..2..2..2
Showing 1-6 of 6 results.

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

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