A266428 -id:A266428 - cp's OEIS frontend

A266423 Number of n X 3 binary arrays with rows and columns lexicographically nondecreasing and column sums nondecreasing.

4, 14, 39, 96, 212, 433, 826, 1493, 2575, 4270, 6841, 10639, 16114, 23845, 34555, 49147, 68725, 94637, 128501, 172257, 228199, 299035, 387927, 498560, 635189, 802719, 1006760, 1253717, 1550855, 1906400, 2329613, 2830904, 3421916, 4115651

Offset: 1

R. H. Hardin, Dec 29 2015

nonn

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

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

Column 3 of A266428.

Empirical: a(n) = 5*a(n-1) - 8*a(n-2) + a(n-3) + 9*a(n-4) - 6*a(n-5) - 6*a(n-7) + 9*a(n-8) + a(n-9) - 8*a(n-10) + 5*a(n-11) - a(n-12).

Empirical g.f.: x*(4 - 6*x + x^2 + 9*x^3 - 6*x^4 - 6*x^6 + 9*x^7 + x^8 - 8*x^9 + 5*x^10 - x^11) / ((1 - x)^8*(1 + x)^2*(1 + x + x^2)). - Colin Barker, Jan 09 2019

A266424 Number of nX4 binary arrays with rows and columns lexicographically nondecreasing and column sums nondecreasing.

Original entry on oeis.org

5, 25, 106, 404, 1391, 4383, 12758, 34611, 88206, 212609, 487630, 1069664, 2254259, 4581719, 9011222, 17200214, 31944220, 57853902, 102380657, 177341666, 301156443, 502075951, 822789263, 1326908069, 2107999291, 3302022425

Offset: 1

R. H. Hardin, Dec 29 2015

nonn

Column 4 of A266428.

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

R. H. Hardin, Table of n, a(n) for n = 1..66

Cf. A266428.

A266425 Number of nX5 binary arrays with rows and columns lexicographically nondecreasing and column sums nondecreasing.

Original entry on oeis.org

6, 41, 259, 1556, 8764, 45907, 223075, 1005991, 4224203, 16588684, 61226525, 213418690, 705807396, 2223963956, 6702140026, 19383434369, 53965133477, 145029252226, 377163396856, 951257706522, 2331468492530, 5562985385965

Offset: 1

R. H. Hardin, Dec 29 2015

nonn

Column 5 of A266428.

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

R. H. Hardin, Table of n, a(n) for n = 1..31

Cf. A266428.

A266429 Number of 3 X n binary arrays with rows and columns lexicographically nondecreasing and column sums nondecreasing.

Original entry on oeis.org

4, 13, 39, 106, 259, 574, 1170, 2223, 3982, 6787, 11089, 17472, 26677, 39628, 57460, 81549, 113544, 155401, 209419, 278278, 365079, 473386, 607270, 771355, 970866, 1211679, 1500373, 1844284, 2251561, 2731224, 3293224, 3948505, 4709068, 5588037

Offset: 1

R. H. Hardin, Dec 29 2015

nonn

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

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

Row 3 of A266428.

Empirical: a(n) = (1/360)*n^6 + (1/40)*n^5 + (1/9)*n^4 + (7/24)*n^3 + (319/360)*n^2 + (101/60)*n + 1.
Conjectures from Colin Barker, Jan 09 2019: (Start)
G.f.: x*(4 - 15*x + 32*x^2 - 34*x^3 + 21*x^4 - 7*x^5 + x^6) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
(End)

A266430 Number of 4 X n binary arrays with rows and columns lexicographically nondecreasing and column sums nondecreasing.

Original entry on oeis.org

5, 22, 96, 404, 1556, 5365, 16585, 46463, 119452, 285124, 638247, 1351194, 2724385, 5262379, 9785590, 17590461, 30674359, 52045522, 86143170, 139398464, 220973442, 343722465, 525429159, 790381435, 1171358006, 1712112000, 2470450897

Offset: 1

R. H. Hardin, Dec 29 2015

nonn

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

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

Row 4 of A266428.

Empirical: a(n) = (1/9979200)*n^11 + (1/201600)*n^10 + (1/12096)*n^9 + (1/1344)*n^8 + (1271/302400)*n^7 + (479/28800)*n^6 + (12797/181440)*n^5 + (97/504)*n^4 + (1779/2800)*n^3 + (2032/1575)*n^2 + (8269/4620)*n + 1.
Conjectures from Colin Barker, Jan 09 2019: (Start)
G.f.: x*(5 - 38*x + 162*x^2 - 396*x^3 + 679*x^4 - 833*x^5 + 737*x^6 - 471*x^7 + 213*x^8 - 65*x^9 + 12*x^10 - x^11) / (1 - x)^12.
a(n) = 12*a(n-1) - 66*a(n-2) + 220*a(n-3) - 495*a(n-4) + 792*a(n-5) - 924*a(n-6) + 792*a(n-7) - 495*a(n-8) + 220*a(n-9) - 66*a(n-10) + 12*a(n-11) - a(n-12) for n>12.
(End)

A266431 Number of 5Xn binary arrays with rows and columns lexicographically nondecreasing and column sums nondecreasing.

Original entry on oeis.org

6, 34, 212, 1391, 8764, 49894, 251381, 1122721, 4490732, 16284683, 54165714, 166968275, 481237398, 1306708520, 3364174219, 8257222586, 19412425379, 43890267973, 95767324137, 202278568268, 414691101885, 827108931171

Offset: 1

R. H. Hardin, Dec 29 2015

nonn

Row 5 of A266428.

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

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

Cf. A266428.

Empirical: a(n) = (1/7602818775552000)*n^19 + (1/47076277248000)*n^18 + (389/266765571072000)*n^17 + (47/815173632000)*n^16 + (11629/7846046208000)*n^15 + (413249/15692092416000)*n^14 + (7941701/23538138624000)*n^13 + (23266079/7242504192000)*n^12 + (14091433/603542016000)*n^11 + (267047/1959552000)*n^10 + (794703337/1207084032000)*n^9 + (14650018639/4828336128000)*n^8 + (267287875667/23538138624000)*n^7 + (102484112767/2139830784000)*n^6 + (39001810891/326918592000)*n^5 + (73310538271/186810624000)*n^4 + (87546462023/102918816000)*n^3 + (113077535/72648576)*n^2 + (469781209/232792560)*n + 1

A266432 Number of 6Xn binary arrays with rows and columns lexicographically nondecreasing and column sums nondecreasing.

Original entry on oeis.org

7, 50, 433, 4383, 45907, 448649, 3889553, 29520031, 197001842, 1168481498, 6234449897, 30265682491, 135048855227, 558800630541, 2160517610564, 7856777499625, 27025799141430, 88367939113010, 275837411169430

Offset: 1

R. H. Hardin, Dec 29 2015

nonn

Row 6 of A266428.

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical polynomial of degree 33

Cf. A266428.

Empirical polynomial of degree 33 (see link above)

A266433 Number of 7Xn binary arrays with rows and columns lexicographically nondecreasing and column sums nondecreasing.

Original entry on oeis.org

8, 70, 826, 12758, 223075, 3825307, 59155748, 798834778, 9379683461, 96481143688, 879275711012, 7183343579974, 53182973236784, 360298764101463, 2252503422916387, 13090825673375302, 71176326297105679, 364068218093477268

Offset: 1

R. H. Hardin, Dec 29 2015

nonn

Row 7 of A266428.

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical polynomial of degree 57

Cf. A266428.

Empirical polynomial of degree 57 (see link above)

A266422 Number of n X n binary arrays with rows and columns lexicographically nondecreasing and column sums nondecreasing.

Original entry on oeis.org

2, 7, 39, 404, 8764, 448649, 59155748, 21325003746, 21901867532457, 66087854484252677, 600640567173169508177

Offset: 1

R. H. Hardin, Dec 29 2015

nonn

Diagonal of A266428.

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

Cf. A266428.

A266426 Number of nX6 binary arrays with rows and columns lexicographically nondecreasing and column sums nondecreasing.

Original entry on oeis.org

7, 63, 574, 5365, 49894, 448649, 3825307, 30555624, 227542455, 1579153474, 10236107278, 62184207773, 355425984636, 1918894455423, 9822580592133, 47841257692021, 222427734697477, 990076818618586

Offset: 1

R. H. Hardin, Dec 29 2015

nonn

Column 6 of A266428.

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

Cf. A266428.

cp's OEIS Frontend

A266423 Number of n X 3 binary arrays with rows and columns lexicographically nondecreasing and column sums nondecreasing.

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A266424 Number of nX4 binary arrays with rows and columns lexicographically nondecreasing and column sums nondecreasing.

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A266425 Number of nX5 binary arrays with rows and columns lexicographically nondecreasing and column sums nondecreasing.

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A266429 Number of 3 X n binary arrays with rows and columns lexicographically nondecreasing and column sums nondecreasing.

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A266430 Number of 4 X n binary arrays with rows and columns lexicographically nondecreasing and column sums nondecreasing.

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A266431 Number of 5Xn binary arrays with rows and columns lexicographically nondecreasing and column sums nondecreasing.

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A266432 Number of 6Xn binary arrays with rows and columns lexicographically nondecreasing and column sums nondecreasing.

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A266433 Number of 7Xn binary arrays with rows and columns lexicographically nondecreasing and column sums nondecreasing.

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A266422 Number of n X n binary arrays with rows and columns lexicographically nondecreasing and column sums nondecreasing.

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A266426 Number of nX6 binary arrays with rows and columns lexicographically nondecreasing and column sums nondecreasing.

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