A266547 -id:A266547 - cp's OEIS frontend

A266542 Number of n X 3 binary arrays with rows and columns lexicographically nondecreasing and row and column sums nonincreasing.

2, 3, 5, 6, 8, 11, 13, 16, 20, 23, 27, 32, 36, 41, 47, 52, 58, 65, 71, 78, 86, 93, 101, 110, 118, 127, 137, 146, 156, 167, 177, 188, 200, 211, 223, 236, 248, 261, 275, 288, 302, 317, 331, 346, 362, 377, 393, 410, 426, 443, 461, 478, 496, 515, 533, 552, 572, 591, 611, 632

Offset: 1

R. H. Hardin, Dec 31 2015

nonn

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

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

Column 3 of A266547.

Empirical: a(n) = 2*a(n-1) - a(n-2) + a(n-3) - 2*a(n-4) + a(n-5).

Empirical g.f.: x*(2 - x + x^2 - 3*x^3 + 2*x^4) / ((1 - x)^3*(1 + x + x^2)). - Colin Barker, Jan 10 2019

A266543 Number of n X 4 binary arrays with rows and columns lexicographically nondecreasing and row and column sums nonincreasing.

Original entry on oeis.org

2, 4, 6, 12, 16, 27, 36, 57, 76, 114, 149, 213, 276, 379, 485, 645, 811, 1051, 1304, 1652, 2021, 2511, 3034, 3709, 4431, 5338, 6311, 7510, 8795, 10352, 12020, 14010, 16142, 18653, 21340, 24469, 27813, 31669, 35786, 40492, 45507, 51196, 57252, 64073, 71324

Offset: 1

R. H. Hardin, Dec 31 2015

nonn

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

R. H. Hardin, Table of n, a(n) for n = 1..179

Column 4 of A266547.

Empirical: a(n) = a(n-1) + 2*a(n-2) - a(n-3) - a(n-4) - a(n-5) - a(n-6) + 2*a(n-8) + 2*a(n-9) - a(n-11) - a(n-12) - a(n-13) - a(n-14) + 2*a(n-15) + a(n-16) - a(n-17).

Empirical g.f.: x*(2 + 2*x - 2*x^2 - 2*x^4 - x^5 + x^6 + 5*x^7 + 4*x^8 + 3*x^9 - x^10 - 2*x^11 - 2*x^12 - x^13 + 4*x^14 + 2*x^15 - 2*x^16) / ((1 - x)^6*(1 + x)^3*(1 + x^2)*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)). - Colin Barker, Jan 10 2019

A266544 Number of nX5 binary arrays with rows and columns lexicographically nondecreasing and row and column sums nonincreasing.

Original entry on oeis.org

2, 4, 8, 16, 36, 58, 110, 196, 363, 695, 1157, 2023, 3446, 5755, 9485, 14901, 23156, 35568, 53350, 79575, 114919, 165223, 233650, 327246, 453231, 618603, 836533, 1122433, 1490044, 1967385, 2565448, 3329153, 4284884, 5482977, 6970961, 8800503

Offset: 1

R. H. Hardin, Dec 31 2015

nonn

Column 5 of A266547.

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

R. H. Hardin, Table of n, a(n) for n = 1..60

Cf. A266547.

A266541 Number of n X n binary arrays with rows and columns lexicographically nondecreasing and row and column sums nonincreasing.

Original entry on oeis.org

2, 3, 5, 12, 36, 176, 1688, 48167, 4283651

Offset: 1

R. H. Hardin, Dec 31 2015

nonn

Diagonal of A266547.

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

Cf. A266547.

A266545 Number of nX6 binary arrays with rows and columns lexicographically nondecreasing and row and column sums nonincreasing.

Original entry on oeis.org

2, 5, 11, 27, 58, 176, 366, 1062, 2571, 7345, 17540, 47970, 109375, 272134, 595031, 1359839, 2827311, 6072251, 12027150, 24388681, 46416427, 89575530, 164016985, 303788687, 537614351, 959313275, 1647205384

Offset: 1

R. H. Hardin, Dec 31 2015

nonn

Column 6 of A266547.

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

Cf. A266547.

A266546 Number of nX7 binary arrays with rows and columns lexicographically nondecreasing and row and column sums nonincreasing.

Original entry on oeis.org

2, 5, 13, 36, 110, 366, 1688, 5312, 24921, 101495, 417118, 1673507, 6081357, 22843019, 72935735, 238112928, 734665224, 2185350505

Offset: 1

R. H. Hardin, Dec 31 2015

nonn

Column 7 of A266547.

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

Cf. A266547.

cp's OEIS Frontend

A266542 Number of n X 3 binary arrays with rows and columns lexicographically nondecreasing and row and column sums nonincreasing.

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A266543 Number of n X 4 binary arrays with rows and columns lexicographically nondecreasing and row and column sums nonincreasing.

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A266544 Number of nX5 binary arrays with rows and columns lexicographically nondecreasing and row and column sums nonincreasing.

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A266541 Number of n X n binary arrays with rows and columns lexicographically nondecreasing and row and column sums nonincreasing.

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A266545 Number of nX6 binary arrays with rows and columns lexicographically nondecreasing and row and column sums nonincreasing.

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A266546 Number of nX7 binary arrays with rows and columns lexicographically nondecreasing and row and column sums nonincreasing.

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