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.

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A250759 Number of (4+1) X (n+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)+x(i-1,j) in the j direction.

Original entry on oeis.org

1029, 2361, 4239, 6663, 9633, 13149, 17211, 21819, 26973, 32673, 38919, 45711, 53049, 60933, 69363, 78339, 87861, 97929, 108543, 119703, 131409, 143661, 156459, 169803, 183693, 198129, 213111, 228639, 244713, 261333, 278499, 296211, 314469
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Examples

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

Links

Crossrefs

Row 4 of A250755.

Formula

Empirical: a(n) = 273*n^2 + 513*n + 243.
Conjectures from Colin Barker, Nov 18 2018: (Start)
G.f.: 3*x*(343 - 242*x + 81*x^2) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3.
(End)

A250760 Number of (5+1) X (n+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)+x(i-1,j) in the j direction.

Original entry on oeis.org

3152, 7272, 13089, 20603, 29814, 40722, 53327, 67629, 83628, 101324, 120717, 141807, 164594, 189078, 215259, 243137, 272712, 303984, 336953, 371619, 407982, 446042, 485799, 527253, 570404, 615252, 661797, 710039, 759978, 811614, 864947
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Examples

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

Links

Crossrefs

Row 5 of A250755.

Formula

Empirical: a(n) = (1697/2)*n^2 + (3149/2)*n + 729.
Conjectures from Colin Barker, Nov 18 2018: (Start)
G.f.: x*(3152 - 2184*x + 729*x^2) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3.
(End)

A250761 Number of (6+1) X (n+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)+x(i-1,j) in the j direction.

Original entry on oeis.org

9585, 22197, 40023, 63063, 91317, 124785, 163467, 207363, 256473, 310797, 370335, 435087, 505053, 580233, 660627, 746235, 837057, 933093, 1034343, 1140807, 1252485, 1369377, 1491483, 1618803, 1751337, 1889085, 2032047, 2180223, 2333613
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Examples

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

Links

Crossrefs

Row 6 of A250755.

Formula

Empirical: a(n) = 2607*n^2 + 4791*n + 2187.
Conjectures from Colin Barker, Nov 18 2018: (Start)
G.f.: 3*x*(3195 - 2186*x + 729*x^2) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3.
(End)

A250762 Number of (7+1) X (n+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)+x(i-1,j) in the j direction.

Original entry on oeis.org

29012, 67356, 121593, 191723, 277746, 379662, 497471, 631173, 780768, 946256, 1127637, 1324911, 1538078, 1767138, 2012091, 2272937, 2549676, 2842308, 3150833, 3475251, 3815562, 4171766, 4543863, 4931853, 5335736, 5755512, 6191181, 6642743
Offset: 1

Views

Author

R. H. Hardin, Nov 27 2014

Keywords

Examples

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

Links

Crossrefs

Row 7 of A250755.

Formula

Empirical: a(n) = (15893/2)*n^2 + (29009/2)*n + 6561.
Conjectures from Colin Barker, Nov 18 2018: (Start)
G.f.: x*(29012 - 19680*x + 6561*x^2) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3.
(End)
Previous Showing 11-14 of 14 results.

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