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 1-7 of 7 results.

A252931 Number of n X n nonnegative integer arrays with upper left 0 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, 5, 44, 711, 17962, 578342, 21312696, 857248091, 36723156004, 1650365159314, 77015673357558, 3704833216794534, 182732875391479366, 9203662331845611018, 471886132793225715184, 24568007717042452684419, 1296265434331412271116602
Offset: 1

Views

Author

R. H. Hardin, Dec 24 2014

Keywords

Comments

Diagonal of A252938

Examples

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

Links

A252932 Number of n X 2 nonnegative integer arrays with upper left 0 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

2, 5, 13, 34, 83, 176, 329, 558, 879, 1308, 1861, 2554, 3403, 4424, 5633, 7046, 8679, 10548, 12669, 15058, 17731, 20704, 23993, 27614, 31583, 35916, 40629, 45738, 51259, 57208, 63601, 70454, 77783, 85604, 93933, 102786, 112179, 122128, 132649, 143758
Offset: 1

Views

Author

R. H. Hardin, Dec 24 2014

Keywords

Examples

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

Links

Crossrefs

Column 2 of A252938.

Formula

Empirical: a(n) = (8/3)*n^3 - 18*n^2 + (145/3)*n - 42 for n>2.
Conjectures from Colin Barker, Dec 07 2018: (Start)
G.f.: x*(2 - 3*x + 5*x^2 + 4*x^3 + 7*x^4 + x^5) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>6.
(End)

A252933 Number of n X 3 nonnegative integer arrays with upper left 0 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, 13, 44, 153, 494, 1343, 3016, 5833, 10114, 16179, 24348, 34941, 48278, 64679, 84464, 107953, 135466, 167323, 203844, 245349, 292158, 344591, 402968, 467609, 538834, 616963, 702316, 795213, 895974, 1004919, 1122368, 1248641, 1384058
Offset: 1

Views

Author

R. H. Hardin, Dec 24 2014

Keywords

Examples

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

Links

Crossrefs

Column 3 of A252938.

Formula

Empirical: a(n) = (160/3)*n^3 - 548*n^2 + (6071/3)*n - 2591 for n>4.
Conjectures from Colin Barker, Dec 07 2018: (Start)
G.f.: x*(4 - 3*x + 16*x^2 + 39*x^3 + 98*x^4 + 122*x^5 + 40*x^6 + 4*x^7) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>8.
(End)

A252934 Number of n X 4 nonnegative integer arrays with upper left 0 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

8, 34, 153, 711, 3067, 10920, 30818, 70640, 138558, 242764, 391450, 592808, 855030, 1186308, 1594834, 2088800, 2676398, 3365820, 4165258, 5082904, 6126950, 7305588, 8627010, 10099408, 11730974, 13529900, 15504378, 17662600, 20012758, 22563044
Offset: 1

Views

Author

R. H. Hardin, Dec 24 2014

Keywords

Examples

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

Links

Crossrefs

Column 4 of A252938.

Formula

Empirical: a(n) = (4096/3)*n^3 - 18720*n^2 + (269642/3)*n - 149376 for n>6.
Conjectures from Colin Barker, Dec 07 2018: (Start)
G.f.: x*(8 + 2*x + 65*x^2 + 271*x^3 + 1013*x^4 + 2340*x^5 + 2849*x^6 + 1331*x^7 + 293*x^8 + 20*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)

A252935 Number of n X 5 nonnegative integer arrays with upper left 0 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

15, 83, 494, 3067, 17962, 86488, 320270, 917811, 2127013, 4211511, 7437417, 12070971, 18378413, 26625983, 37079921, 50006467, 65671861, 84342343, 106284153, 131763531, 161046717, 194399951, 232089473, 274381523, 321542341
Offset: 1

Views

Author

R. H. Hardin, Dec 24 2014

Keywords

Examples

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

Links

Crossrefs

Column 5 of A252938.

Formula

Empirical: a(n) = (133120/3)*n^3 - 760496*n^2 + (13526246/3)*n - 9199709 for n>8.
Conjectures from Colin Barker, Dec 07 2018: (Start)
G.f.: x*(15 + 23*x + 252*x^2 + 1529*x^3 + 8341*x^4 + 31149*x^5 + 70316*x^6 + 86878*x^7 + 49399*x^8 + 15733*x^9 + 2477*x^10 + 128*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)

A252936 Number of nX6 nonnegative integer arrays with upper left 0 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

26, 176, 1343, 10920, 86488, 578342, 2952734, 11219797, 32649081, 76641323, 153453179, 273544411, 447399739, 685504923, 998345723, 1396407899, 1890177211, 2490139419, 3206780283, 4050585563, 5032041019, 6161632411, 7449845499
Offset: 1

Views

Author

R. H. Hardin, Dec 24 2014

Keywords

Comments

Column 6 of A252938

Examples

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

Links

Formula

Empirical: a(n) = (5242880/3)*n^3 - 36032512*n^2 + (765093664/3)*n - 618047397 for n>10

A252937 Number of nX7 nonnegative integer arrays with upper left 0 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

42, 329, 3016, 30818, 320270, 2952734, 21312696, 113154831, 440052087, 1302939451, 3104860285, 6297578921, 11347942213, 18725672417, 28900783485, 42343299609, 59523244981, 80910643793, 106975520237, 138187898505
Offset: 1

Views

Author

R. H. Hardin, Dec 24 2014

Keywords

Comments

Column 7 of A252938

Examples

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

Links

Formula

Empirical: a(n) = (235012096/3)*n^3 - 1891478912*n^2 + (46791365972/3)*n - 43861899175 for n>12
Showing 1-7 of 7 results.

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

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