A201700 -id:A201700 - cp's OEIS frontend

A201695 Number of n X 3 0..2 arrays with rows and columns lexicographically nondecreasing read forwards and nonincreasing read backwards.

3, 18, 116, 395, 989, 2068, 3838, 6541, 10455, 15894, 23208, 32783, 45041, 60440, 79474, 102673, 130603, 163866, 203100, 248979, 302213, 363548, 433766, 513685, 604159, 706078, 820368, 947991, 1089945, 1247264, 1421018, 1612313, 1822291

Offset: 1

R. H. Hardin, Dec 03 2011

nonn

Column 3 of A201700.

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A201700.

Empirical: a(n) = (3/2)*n^4 + (4/3)*n^3 - 4*n^2 - (29/6)*n + 9.
Conjectures from Colin Barker, May 23 2018: (Start)
G.f.: x*(3 + 3*x + 56*x^2 - 35*x^3 + 9*x^4) / (1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
(End)

A201696 Number of n X 4 0..2 arrays with rows and columns lexicographically nondecreasing read forwards and nonincreasing read backwards.

Original entry on oeis.org

3, 27, 395, 4998, 35390, 167625, 607919, 1826778, 4775228, 11211034, 24167306, 48600665, 92261185, 166831642, 289389192, 484248471, 785251265, 1238574341, 1906133765, 2869671064, 4235613920, 6140811719, 8759254221, 12309889872

Offset: 1

R. H. Hardin, Dec 03 2011

nonn

Column 4 of A201700.

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A201700.

Empirical: a(n) = (1/907200)*n^10 + (13/20160)*n^9 + (8321/120960)*n^8 + (97/105)*n^7 - (40969/5400)*n^6 + (22681/960)*n^5 - (11661313/362880)*n^4 - (388097/10080)*n^3 + (4320179/16800)*n^2 - (323861/840)*n + 185.
Conjectures from Colin Barker, May 23 2018: (Start)
G.f.: x*(3 - 6*x + 263*x^2 + 1643*x^3 - 1328*x^4 - 4426*x^5 + 5086*x^6 - 1972*x^7 + 1789*x^8 - 1233*x^9 + 185*x^10) / (1 - x)^11.
a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11) for n>11.
(End)

A201697 Number of nX5 0..2 arrays with rows and columns lexicographically nondecreasing read forwards and nonincreasing read backwards.

Original entry on oeis.org

3, 37, 989, 35390, 930564, 14268351, 142436489, 1034563890, 5898023820, 27803725006, 112491133042, 401503571755, 1290797861479, 3798580774670, 10363168825912, 26478119492263, 63883865534377, 146539437113683

Offset: 1

R. H. Hardin Dec 03 2011

nonn

Column 5 of A201700

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Empirical: a(n) = (39619/523069747200)*n^16 + (4468181/653837184000)*n^15 + (29013757/130767436800)*n^14 + (1283689/849139200)*n^13 - (51508993/2874009600)*n^12 - (43603801/256608000)*n^11 + (2874162577/914457600)*n^10 - (7499289487/457228800)*n^9 + (16169769137/731566080)*n^8 + (30409918103/653184000)*n^7 + (408990763441/718502400)*n^6 - (175356370649/25660800)*n^5 + (317152595889599/10897286400)*n^4 - (27799492117129/412776000)*n^3 + (2720484273811/30270240)*n^2 - (23317530409/360360)*n + 19289

A201698 Number of nX6 0..2 arrays with rows and columns lexicographically nondecreasing read forwards and nonincreasing read backwards.

Original entry on oeis.org

3, 48, 2068, 167625, 14268351, 795339012, 27102769900, 615440785548, 10106227864338, 127441635892627, 1290114077123683, 10846768837607450, 77797729805055016, 486398599750167133, 2697872438447793007

Offset: 1

R. H. Hardin Dec 03 2011

nonn

Column 6 of A201700

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

R. H. Hardin, Table of n, a(n) for n = 1..90

Empirical: a(n) is a polynomial of degree 34

A201699 Number of nX7 0..2 arrays with rows and columns lexicographically nondecreasing read forwards and nonincreasing read backwards.

Original entry on oeis.org

3, 60, 3838, 607919, 142436489, 27102769900, 3262897246338, 253484699853930, 13657827589827288, 542530203631847499, 16634470482072064655, 407700696414920035296, 8211702473582080609860, 139013768818199221546289

Offset: 1

R. H. Hardin Dec 03 2011

nonn

Column 7 of A201700

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

R. H. Hardin, Table of n, a(n) for n = 1..22

A201694 Number of n X n 0..2 arrays with rows and columns lexicographically nondecreasing read forwards and nonincreasing read backwards.

Original entry on oeis.org

3, 10, 116, 4998, 930564, 795339012, 3262897246338

Offset: 1

R. H. Hardin Dec 03 2011

nonn

Diagonal of A201700

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

cp's OEIS Frontend

A201695 Number of n X 3 0..2 arrays with rows and columns lexicographically nondecreasing read forwards and nonincreasing read backwards.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A201696 Number of n X 4 0..2 arrays with rows and columns lexicographically nondecreasing read forwards and nonincreasing read backwards.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A201697 Number of nX5 0..2 arrays with rows and columns lexicographically nondecreasing read forwards and nonincreasing read backwards.

Views

Author

Keywords

Comments

Examples

Links

Formula

A201698 Number of nX6 0..2 arrays with rows and columns lexicographically nondecreasing read forwards and nonincreasing read backwards.

Views

Author

Keywords

Comments

Examples

Links

Formula

A201699 Number of nX7 0..2 arrays with rows and columns lexicographically nondecreasing read forwards and nonincreasing read backwards.

Views

Author

Keywords

Comments

Examples

Links

A201694 Number of n X n 0..2 arrays with rows and columns lexicographically nondecreasing read forwards and nonincreasing read backwards.

Views

Author

Keywords

Comments

Examples