A266935 -id:A266935 - cp's OEIS frontend

A266930 Number of n X 3 binary arrays with rows lexicographically nondecreasing and columns lexicographically nondecreasing and row sums nondecreasing and column sums nonincreasing.

2, 4, 9, 20, 44, 92, 182, 340, 605, 1028, 1680, 2651, 4058, 6045, 8793, 12518, 17484, 24001, 32438, 43222, 56853, 73901, 95024, 120965, 152570, 190786, 236681, 291440, 356388, 432986, 522854, 627768, 749685, 890738, 1053264, 1239799, 1453106

Offset: 1

R. H. Hardin, Jan 06 2016

nonn

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

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

Column 3 of A266935.

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

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

A266931 Number of n X 4 binary arrays with rows lexicographically nondecreasing and columns lexicographically nondecreasing and row sums nondecreasing and column sums nonincreasing.

Original entry on oeis.org

2, 5, 12, 35, 100, 288, 794, 2077, 5110, 11869, 26086, 54543, 108999, 209148, 386883, 692473, 1203061, 2034487, 3357115, 5416951, 8563297, 13284702, 20254831, 30390893, 44926915, 65505045, 94288435, 134099783, 188589873, 262441858

Offset: 1

R. H. Hardin, Jan 06 2016

nonn

Column 4 of A266935.

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

R. H. Hardin, Table of n, a(n) for n = 1..64

Cf. A266935.

Empirical: a(n) = 2*a(n-1) +3*a(n-2) -4*a(n-3) -9*a(n-4) -a(n-5) +19*a(n-6) +13*a(n-7) -13*a(n-8) -25*a(n-9) -11*a(n-10) +15*a(n-11) +22*a(n-12) +17*a(n-13) -4*a(n-14) -23*a(n-15) -23*a(n-16) -4*a(n-17) +17*a(n-18) +22*a(n-19) +15*a(n-20) -11*a(n-21) -25*a(n-22) -13*a(n-23) +13*a(n-24) +19*a(n-25) -a(n-26) -9*a(n-27) -4*a(n-28) +3*a(n-29) +2*a(n-30) -a(n-31).

A266932 Number of nX5 binary arrays with rows lexicographically nondecreasing and columns lexicographically nondecreasing and row sums nondecreasing and column sums nonincreasing.

Original entry on oeis.org

2, 5, 14, 52, 210, 871, 3566, 13899, 50841, 173470, 553021, 1652621, 4652572, 12400392, 31443461, 76188169, 177120011, 396481264, 857322183, 1795814448, 3653191802, 7233526075, 13969016501, 26357103244, 48668165412, 88071764221

Offset: 1

R. H. Hardin, Jan 06 2016

nonn

Column 5 of A266935.

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

R. H. Hardin, Table of n, a(n) for n = 1..34

Cf. A266935.

A266936 Number of 3 X n binary arrays with rows lexicographically nondecreasing and columns lexicographically nondecreasing and row sums nondecreasing and column sums nonincreasing.

Original entry on oeis.org

4, 7, 9, 12, 14, 19, 21, 26, 30, 35, 39, 46, 50, 57, 63, 70, 76, 85, 91, 100, 108, 117, 125, 136, 144, 155, 165, 176, 186, 199, 209, 222, 234, 247, 259, 274, 286, 301, 315, 330, 344, 361, 375, 392, 408, 425, 441, 460, 476, 495, 513, 532, 550, 571, 589, 610, 630, 651, 671

Offset: 1

R. H. Hardin, Jan 06 2016

nonn

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

R. H. Hardin, Table of n, a(n) for n = 1..158

Row 3 of A266935.

Empirical: a(n) = a(n-1) + a(n-2) - a(n-4) - a(n-5) + a(n-6).

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

A266937 Number of 4 X n binary arrays with rows lexicographically nondecreasing and columns lexicographically nondecreasing and row sums nondecreasing and column sums nonincreasing.

Original entry on oeis.org

5, 12, 20, 35, 52, 82, 115, 169, 232, 322, 426, 573, 738, 961, 1215, 1543, 1912, 2382, 2905, 3557, 4280, 5161, 6135, 7308, 8594, 10120, 11791, 13749, 15883, 18361, 21049, 24142, 27490, 31307, 35427, 40093, 45111, 50757, 56818, 63594, 70848, 78917, 87535

Offset: 1

R. H. Hardin, Jan 06 2016

nonn

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

R. H. Hardin, Table of n, a(n) for n = 1..87

Row 4 of A266935.

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*(5 + 7*x - 2*x^2 - 4*x^3 - 6*x^4 - 3*x^5 + x^6 + 9*x^7 + 12*x^8 + 2*x^9 -6*x^10 - 4*x^11 - 6*x^12 - 5*x^13 + 9*x^14 + 6*x^15 - 5*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

A266938 Number of 5Xn binary arrays with rows lexicographically nondecreasing and columns lexicographically nondecreasing and row sums nondecreasing and column sums nonincreasing.

Original entry on oeis.org

6, 19, 44, 100, 210, 429, 816, 1534, 2727, 4753, 7931, 13044, 20676, 32360, 49327, 73959, 108612, 157751, 224746, 317514, 440564, 606496, 823905, 1110469, 1480403, 1957027, 2563177, 3335398, 4302564, 5520403, 7021711, 8888187, 11173884

Offset: 1

R. H. Hardin, Jan 06 2016

nonn

Row 5 of A266935.

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

R. H. Hardin, Table of n, a(n) for n = 1..57

Cf. A266935.

A266929 Number of n X n binary arrays with rows lexicographically nondecreasing and columns lexicographically nondecreasing and row sums nondecreasing and column sums nonincreasing.

Original entry on oeis.org

2, 4, 9, 35, 210, 2577, 68890, 4605960, 821453747

Offset: 1

R. H. Hardin, Jan 06 2016

nonn

Diagonal of A266935.

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

Cf. A266935.

A266933 Number of nX6 binary arrays with rows lexicographically nondecreasing and columns lexicographically nondecreasing and row sums nondecreasing and column sums nonincreasing.

Original entry on oeis.org

2, 6, 19, 82, 429, 2577, 15850, 96503, 555060, 2977370, 14782970, 68041108, 291292442, 1165800099, 4383605127, 15564591521, 52423001756, 168200350788, 516045791503, 1519124991181

Offset: 1

R. H. Hardin, Jan 06 2016

nonn

Column 6 of A266935.

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

Cf. A266935.

A266934 Number of nX7 binary arrays with rows lexicographically nondecreasing and columns lexicographically nondecreasing and row sums nondecreasing and column sums nonincreasing.

Original entry on oeis.org

2, 6, 21, 115, 816, 7185, 68890, 671796, 6347005, 56180274, 460040399, 3470013146, 24151911854, 155703390684

Offset: 1

R. H. Hardin, Jan 06 2016

nonn

Column 7 of A266935.

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

Cf. A266935.

A266939 Number of 6Xn binary arrays with rows lexicographically nondecreasing and columns lexicographically nondecreasing and row sums nondecreasing and column sums nonincreasing.

Original entry on oeis.org

7, 29, 92, 288, 871, 2577, 7185, 19529, 50216, 125786, 298869, 696808, 1546941, 3382516, 7085876, 14650326, 29153966, 57417292, 109223923, 205966389, 376634957, 683318087, 1206075185, 2114385852, 3615867548

Offset: 1

R. H. Hardin, Jan 06 2016

nonn

Row 6 of A266935.

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

Cf. A266935.

cp's OEIS Frontend

A266930 Number of n X 3 binary arrays with rows lexicographically nondecreasing and columns lexicographically nondecreasing and row sums nondecreasing and column sums nonincreasing.

Views

Author

Keywords

Examples

Links

Crossrefs

Formula

A266931 Number of n X 4 binary arrays with rows lexicographically nondecreasing and columns lexicographically nondecreasing and row sums nondecreasing and column sums nonincreasing.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A266932 Number of nX5 binary arrays with rows lexicographically nondecreasing and columns lexicographically nondecreasing and row sums nondecreasing and column sums nonincreasing.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

A266936 Number of 3 X n binary arrays with rows lexicographically nondecreasing and columns lexicographically nondecreasing and row sums nondecreasing and column sums nonincreasing.

Views

Author

Keywords

Examples

Links

Crossrefs

Formula

A266937 Number of 4 X n binary arrays with rows lexicographically nondecreasing and columns lexicographically nondecreasing and row sums nondecreasing and column sums nonincreasing.

Views

Author

Keywords

Examples

Links

Crossrefs

Formula

A266938 Number of 5Xn binary arrays with rows lexicographically nondecreasing and columns lexicographically nondecreasing and row sums nondecreasing and column sums nonincreasing.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

A266929 Number of n X n binary arrays with rows lexicographically nondecreasing and columns lexicographically nondecreasing and row sums nondecreasing and column sums nonincreasing.

Views

Author

Keywords

Comments

Examples

Crossrefs

A266933 Number of nX6 binary arrays with rows lexicographically nondecreasing and columns lexicographically nondecreasing and row sums nondecreasing and column sums nonincreasing.

Views

Author

Keywords

Comments

Examples

Crossrefs

A266934 Number of nX7 binary arrays with rows lexicographically nondecreasing and columns lexicographically nondecreasing and row sums nondecreasing and column sums nonincreasing.

Views

Author

Keywords

Comments

Examples

Crossrefs

A266939 Number of 6Xn binary arrays with rows lexicographically nondecreasing and columns lexicographically nondecreasing and row sums nondecreasing and column sums nonincreasing.

Views

Author

Keywords

Comments

Examples

Crossrefs