A195278 -id:A195278 - cp's OEIS frontend

A195279 Number of lower triangles of a 3 X 3 integer array with each element differing from all of its vertical and horizontal neighbors by n or less and triangles differing by a constant counted only once.

171, 2125, 11319, 39609, 107811, 248261, 507375, 948209, 1653019, 2725821, 4294951, 6515625, 9572499, 13682229, 19096031, 26102241, 35028875, 46246189, 60169239, 77260441, 98032131, 123049125, 152931279, 188356049, 230061051

Offset: 1

R. H. Hardin, Sep 14 2011

nonn

Row 3 of A195278.

			Some solutions for n=5:
...0.........0.........0.........0.........0.........0.........0.........0
..-2.-1......3..4.....-3..1.....-4.-1.....-1..4.....-5.-1......5..8......4..4
..-3.-6.-6...2..1..1..-7.-3..0..-5.-4.-6..-4.-1..3..-7.-2..2...8..5..2...0..0.-2

R. H. Hardin, Table of n, a(n) for n = 1..200

Cf. A195278.

Empirical: a(n) = (64/3)*n^5 + (160/3)*n^4 + 56*n^3 + (92/3)*n^2 + (26/3)*n + 1.
Conjectures from Colin Barker, Mar 01 2018: (Start)
G.f.: x*(171 + 1099*x + 1134*x^2 + 150*x^3 + 7*x^4 - x^5) / (1 - x)^6.
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.
(End)

A195272 Number of lower triangles of an n X n integer array with each element differing from all of its vertical and horizontal neighbors by 2 or less and triangles differing by a constant counted only once.

Original entry on oeis.org

1, 25, 2125, 626525, 649112125, 2375645170875, 30812488814662125, 1419187229961716246975, 232443697109891957009442125, 135513533218801266004475511024825

Offset: 1

R. H. Hardin Sep 14 2011

nonn

Column 2 of A195278

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

R. H. Hardin, Table of n, a(n) for n = 1..11

A195280 Number of lower triangles of a 4X4 integer array with each element differing from all of its vertical and horizontal neighbors by n or less and triangles differing by a constant counted only once.

Original entry on oeis.org

6939, 626525, 12608631, 119743353, 724789395, 3249312469, 11755976175, 36215968241, 98454861067, 242177297229, 548894457959, 1162058315625, 2322243189891, 4416808121541, 8048123047903, 14125147709409, 23983914638075

Offset: 1

R. H. Hardin Sep 14 2011

nonn

Row 4 of A195278

			Some solutions for n=5
...0............0............0............0............0............0
..-1.-2.........1..1.........5..3.........3..1........-1.-3.........3..4
..-6.-5.-6.....-2..2.-1......5..3..1......7..4..2......1..1.-2......0..4..1
..-2.-1.-1..1...3..6..2..0...1.-2..3..1...5..3.-2.-1..-2..2..1..1..-5..0..2..1

R. H. Hardin, Table of n, a(n) for n = 1..169

Empirical: a(n) = (49024/315)*n^9 + (24512/35)*n^8 + (457792/315)*n^7 + (81824/45)*n^6 + (67912/45)*n^5 + (38756/45)*n^4 + (11832/35)*n^3 + (27752/315)*n^2 + (1454/105)*n + 1

A195281 Number of lower triangles of a 5X5 integer array with each element differing from all of its vertical and horizontal neighbors by n or less and triangles differing by a constant counted only once.

Original entry on oeis.org

609309, 649112125, 68604760497, 2266745635377, 37235577669213, 383752106451389, 2834518121474625, 16307551677812033, 77247504140304381, 313215736935324573, 1118258748766971057, 3590779676071640625

Offset: 1

R. H. Hardin Sep 14 2011

nonn

Row 5 of A195278

			Some solutions for n=5
...0...............0...............0...............0...............0
...1..6............3..1...........-2..0............4..3...........-3..0
...0..1..0.........1..1..5........-6.-5-10.........0..5..2........-6.-3.-3
...5..2..0.-5......5..5..1..4.....-3.-5-10.-6......1..3.-2.-6.....-2..2.-2.-5
...7..6..3.-2..3...9..6..1.-1..0..-2.-7.-7.-7.-4...1..0.-2.-4.-1...3..0.-5.-4.-8

R. H. Hardin, Table of n, a(n) for n = 1..39

Empirical: a(n) = (735698944/467775)*n^14 + (735698944/66825)*n^13 + (5736600832/155925)*n^12 + (36310211072/467775)*n^11 + (4906182016/42525)*n^10 + (603389056/4725)*n^9 + (4615314688/42525)*n^8 + (3060288256/42525)*n^7 + (176877304/4725)*n^6 + (647154728/42525)*n^5 + (2229757561/467775)*n^4 + (174277454/155925)*n^3 + (1380143/7425)*n^2 + (68144/3465)*n + 1

A195282 Number of lower triangles of a 6X6 integer array with each element differing from all of its vertical and horizontal neighbors by n or less and triangles differing by a constant counted only once.

Original entry on oeis.org

116330103, 2375645170875, 1833160598134397, 270149651796118149, 14698398557250127027, 411207789366962687359, 7151051711514319493625, 87046671186871404342793, 802793502537221468366191

Offset: 1

R. H. Hardin Sep 14 2011

nonn

Row 6 of A195278

			Some solutions for n=5
...0..................0..................0..................0
..-1.-1...............2..2..............-1..2...............1..3
..-1..1..5............3..2..7...........-3.-1.-5............0.-1.-5
...0..2..6..9.........5..2..2..0........-5.-2..0..1.........4..4..0..2
..-3.-2..1..6..3......0..3..1..2..2.....-5.-6.-5.-2.-5......3..7..3..2..4
..-6.-1.-2..3.-2..1...2..6..4..5..0.-2.-10.-9-10.-5.-1.-3...5..7..6..1..3..7

R. H. Hardin, Table of n, a(n) for n = 1..15

A195283 Number of lower triangles of a 7X7 integer array with each element differing from all of its vertical and horizontal neighbors by n or less and triangles differing by a constant counted only once.

Original entry on oeis.org

48439766655, 30812488814662125, 241338657495589799523, 203368493873412168605037, 44727914263743356875711779, 4011033701337366560359871745, 189393562987102056163761489375

Offset: 1

R. H. Hardin Sep 14 2011

nonn

Row 7 of A195278

			Some solutions for n=5
...0.....................0.....................0
..-2.-6.................-1..2.................-5-10
...1.-4.-2..............-6.-3.-6..............-2.-5.-1
...1.-2..2..7...........-2.-4.-3.-1...........-7.-6.-5..0
..-2.-7.-2..3.-2.........3..0..1..3..0........-9.-8.-8.-5.-9
..-6-10.-6.-1.-5.-4......8..3..0.-1.-5-10.....-8.-6.-5.-9-12-17
..-6.-8.-3..1..0.-4.-3...4..2..4..2.-3.-5.-2.-13-11.-7.-5.-7-12-13

R. H. Hardin, Table of n, a(n) for n = 1..8

A195273 Number of lower triangles of an n X n integer array with each element differing from all of its vertical and horizontal neighbors by 3 or less and triangles differing by a constant counted only once.

Original entry on oeis.org

1, 49, 11319, 12608631, 68604760497, 1833160598134397, 241338657495589799523, 156865927758847103008175635, 504091149328239931994947830412175

Offset: 1

R. H. Hardin Sep 14 2011

nonn

Column 3 of A195278

			Some solutions for n=5
...0...............0...............0...............0...............0
...3..4...........-2..0............2..4............1..2...........-3.-1
...2..5..3........-3..0..3.........3..6..5.........0.-1.-1........-5.-2..1
...0..2..2..2......0..0..0.-1......6..3..6..6......0..2..1..3.....-2..1..3..5
...0..2..5..2..4..-3.-2.-3.-2.-1...6..5..6..8..9..-1..2..1..0.-3..-4.-2..0..2..1

A195274 Number of lower triangles of an n X n integer array with each element differing from all of its vertical and horizontal neighbors by 4 or less and triangles differing by a constant counted only once.

Original entry on oeis.org

1, 81, 39609, 119743353, 2266745635377, 270149651796118149, 203368493873412168605037, 969036564714736790447759054277

Offset: 1

R. H. Hardin Sep 14 2011

nonn

Column 4 of A195278

			Some solutions for n=5
...0...............0...............0...............0...............0
...1..4............1..1............1..0............2..5...........-3.-1
..-1..3..2.........4..3..7.........3..0..4.........1..2..6........-6.-5.-9
..-4.-1..3..7......3..6.10..7......1..2..0.-3......0..0..2..4.....-6.-7.-8-10
...0.-3..0..4..2...4..4..8..9..6...0..3..2..1..4..-4.-4.-1..2..2.-10-10.-8-11-13

A195275 Number of lower triangles of an n X n integer array with each element differing from all of its vertical and horizontal neighbors by 5 or less and triangles differing by a constant counted only once.

Original entry on oeis.org

1, 121, 107811, 724789395, 37235577669213, 14698398557250127027, 44727914263743356875711779, 1051443054205968885835418306282537

Offset: 1

R. H. Hardin Sep 14 2011

nonn

Column 5 of A195278

			Some solutions for n=5
...0...............0...............0...............0...............0
..-5.-5...........-2..3............0..0............0..5...........-3.-4
...0..0.-4........-2.-2.-2.........0.-1.-5.........0..0..3........-1.-4.-3
...3..2.-3.-3.....-1.-4.-3.-8......5..4..0..0......0..2..1..0......1.-2..1..3
...3.-2..1.-1..2...2.-3.-6.-7.-6...9..8..5..1.-4...0..3..2..3..2..-1.-2.-1.-1.-3

A195276 Number of lower triangles of an n X n integer array with each element differing from all of its vertical and horizontal neighbors by 6 or less and triangles differing by a constant counted only once.

Original entry on oeis.org

1, 169, 248261, 3249312469, 383752106451389, 411207789366962687359, 4011033701337366560359871745

Offset: 1

R. H. Hardin Sep 14 2011

nonn

Column 6 of A195278

			Some solutions for n=5
...0...............0...............0...............0...............0
..-6.-1...........-1..3...........-3.-8............3..9...........-2.-7
.-10.-6.-8........-6.-1..3.........1.-5.-8........-1..5..5.........1.-1.-7
.-15-10.-6.-9.....-9.-4.-2.-2......2..1.-2..2......3..7..4..2......1..0.-1..2
.-17-14-12.-9.-8.-10.-8.-4.-2..3...2..4.-1.-4.-6...1..6..4..5..0...5.-1.-7.-2..4

cp's OEIS Frontend

A195279 Number of lower triangles of a 3 X 3 integer array with each element differing from all of its vertical and horizontal neighbors by n or less and triangles differing by a constant counted only once.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A195272 Number of lower triangles of an n X n integer array with each element differing from all of its vertical and horizontal neighbors by 2 or less and triangles differing by a constant counted only once.

Views

Author

Keywords

Comments

Examples

Links

A195280 Number of lower triangles of a 4X4 integer array with each element differing from all of its vertical and horizontal neighbors by n or less and triangles differing by a constant counted only once.

Views

Author

Keywords

Comments

Examples

Links

Formula

A195281 Number of lower triangles of a 5X5 integer array with each element differing from all of its vertical and horizontal neighbors by n or less and triangles differing by a constant counted only once.

Views

Author

Keywords

Comments

Examples

Links

Formula

A195282 Number of lower triangles of a 6X6 integer array with each element differing from all of its vertical and horizontal neighbors by n or less and triangles differing by a constant counted only once.

Views

Author

Keywords

Comments

Examples

Links

A195283 Number of lower triangles of a 7X7 integer array with each element differing from all of its vertical and horizontal neighbors by n or less and triangles differing by a constant counted only once.

Views

Author

Keywords

Comments

Examples

Links

A195273 Number of lower triangles of an n X n integer array with each element differing from all of its vertical and horizontal neighbors by 3 or less and triangles differing by a constant counted only once.

Views

Author

Keywords

Comments

Examples

A195274 Number of lower triangles of an n X n integer array with each element differing from all of its vertical and horizontal neighbors by 4 or less and triangles differing by a constant counted only once.

Views

Author

Keywords

Comments

Examples

A195275 Number of lower triangles of an n X n integer array with each element differing from all of its vertical and horizontal neighbors by 5 or less and triangles differing by a constant counted only once.

Views

Author

Keywords

Comments

Examples

A195276 Number of lower triangles of an n X n integer array with each element differing from all of its vertical and horizontal neighbors by 6 or less and triangles differing by a constant counted only once.

Views

Author

Keywords

Comments

Examples