A233301 -id:A233301 - cp's OEIS frontend

A233302 Number of (2+1) X (n+1) 0..1 arrays x(i,j) with row sums sum{x(i,j), j=1..n+1} nondecreasing, and column sums sum{i^2*x(i,j), i=1..2+1} nondecreasing.

15, 42, 105, 232, 475, 904, 1632, 2806, 4642, 7414, 11500, 17368, 25636, 37054, 52579, 73354, 100799, 136586, 182749, 241654, 316129, 409430, 525392, 668390, 843514, 1056524, 1314050, 1623542, 1993496, 2433398, 2953979, 3567152, 4286297, 5126192

Offset: 1

R. H. Hardin, Dec 07 2013

nonn

Row 2 of A233301, row 3 of A267245.

			Some solutions for n=5:
..0..0..0..0..1..0....1..1..0..0..0..0....0..0..1..0..0..0....0..0..0..0..0..1
..0..0..0..0..0..1....0..0..1..1..1..1....0..0..0..0..0..1....0..1..1..1..1..1
..0..0..0..1..1..1....0..1..1..1..1..1....0..0..0..1..1..1....0..1..1..1..1..1

R. H. Hardin, Table of n, a(n) for n = 1..172

Cf. A233301, A267245.

Empirical: a(n) = 4*a(n-1) - 3*a(n-2) - 7*a(n-3) + 10*a(n-4) + 3*a(n-5) - 6*a(n-6) - 6*a(n-7) + 3*a(n-8) + 10*a(n-9) - 7*a(n-10) - 3*a(n-11) + 4*a(n-12) - a(n-13). - R. H. Hardin, Jan 17 2016.

Empirical g.f.: x*(15 - 18*x - 18*x^2 + 43*x^3 + 6*x^4 - 30*x^5 - 21*x^6 + 22*x^7 + 33*x^8 - 31*x^9 - 8*x^10 + 15*x^11 - 4*x^12) / ((1 - x)^8*(1 + x)^3*(1 + x + x^2)). - Colin Barker, Mar 19 2018

A233303 Number of (3+1)X(n+1) 0..1 arrays x(i,j) with row sums sum{x(i,j), j=1..n+1} nondecreasing, and column sums sum{i^2*x(i,j), i=1..3+1} nondecreasing.

Original entry on oeis.org

31, 141, 567, 1986, 6292, 18205, 48913, 123084, 292784, 662512, 1434508, 2985639, 5997455, 11666253, 22040149, 40541549, 72770415, 127706638, 219494579, 370035418, 612722058, 997726253, 1599424522, 2526675993, 3936943281

Offset: 1

R. H. Hardin, Dec 07 2013

nonn

Row 3 of A233301, row 4 of A267245.

			Some solutions for n=5
..0..0..1..0..0..0....0..1..0..0..0..1....0..0..0..0..0..1....1..1..1..0..0..0
..1..0..0..1..0..0....0..0..0..1..1..1....1..0..1..0..0..1....0..0..0..1..1..1
..1..0..0..0..1..1....0..0..0..1..1..1....0..1..1..0..0..1....1..0..1..1..1..1
..0..1..1..1..1..1....0..0..1..1..1..1....0..0..0..1..1..1....0..1..1..1..1..1

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

A233297 Number of (n+1)X(1+1) 0..1 arrays x(i,j) with row sums sum{x(i,j), j=1..1+1} nondecreasing, and column sums sum{i^2*x(i,j), i=1..n+1} nondecreasing.

Original entry on oeis.org

7, 15, 31, 64, 129, 258, 515, 1029, 2055, 4107, 8211, 16410, 32811, 65624, 131224, 262372, 524634, 1049237, 2098363, 4196161, 8391728, 16783688, 33567165, 67128918, 134250383, 268502449, 536999938, 1073948247, 2147837919, 4295732271

Offset: 1

R. H. Hardin, Dec 07 2013

nonn

Column 1 of A233301

			Some solutions for n=5
..0..0....1..0....1..0....0..0....0..1....0..0....0..1....1..0....1..0....0..0
..0..0....1..0....1..0....0..0....0..1....0..0....1..0....1..0....1..0....0..0
..0..1....0..1....1..0....0..1....0..1....0..0....1..0....1..0....0..1....0..0
..0..1....0..1....0..1....0..1....0..1....1..1....0..1....1..0....0..1....0..0
..1..0....1..0....0..1....0..1....0..1....1..1....1..1....0..1....1..1....0..0
..0..1....0..1....1..1....0..1....1..1....1..1....1..1....0..1....1..1....1..1

R. H. Hardin, Table of n, a(n) for n = 1..36

A233304 Number of (4+1) X (n+1) 0..1 arrays x(i,j) with row sums sum{x(i,j), j=1..n+1} nondecreasing, and column sums sum{i^2*x(i,j), i=1..4+1} nondecreasing.

Original entry on oeis.org

64, 502, 3556, 21957, 122022, 616439, 2871477, 12451710, 50714574, 195371008, 716295219, 2512238327, 8466906587, 27527291020, 86628418167, 264674530948, 787179022872, 2284373978387, 6482027000245, 18018759544172, 49152990387893

Offset: 1

R. H. Hardin, Dec 07 2013

nonn

Row 4 of A233301.

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

R. H. Hardin, Table of n, a(n) for n = 1..25

Cf. A233301.

A233298 Number of (n+1) X (2+1) 0..1 arrays x(i,j) with row sums Sum_{j=1..2+1} x(i,j) nondecreasing, and column sums Sum_{i=1..n+1} i^2*x(i,j) nondecreasing.

Original entry on oeis.org

13, 42, 141, 502, 1739, 5964, 20185, 67609, 224165, 737347, 2407911, 7814616, 25223004, 81015137, 259099567, 825507109, 2621224089, 8298060296, 26197890927, 82506334112, 259260476024

Offset: 1

R. H. Hardin, Dec 07 2013

nonn

Column 2 of A233301.

			Some solutions for n=5
..0..1..0....1..1..0....0..0..0....0..0..0....0..0..1....0..0..0....1..0..0
..1..1..0....1..1..0....0..0..0....0..1..0....0..1..0....0..0..0....0..0..1
..0..1..1....1..0..1....1..0..0....0..0..1....0..1..0....0..0..0....1..1..0
..0..1..1....0..1..1....0..1..0....0..0..1....0..0..1....0..0..0....1..1..0
..1..0..1....0..1..1....0..0..1....0..0..1....1..0..0....0..0..1....1..0..1
..0..1..1....1..1..1....1..1..1....1..1..1....0..1..1....0..1..1....0..1..1

Cf. A233301.

A233299 Number of (n+1)X(3+1) 0..1 arrays x(i,j) with row sums sum{x(i,j), j=1..3+1} nondecreasing, and column sums sum{i^2*x(i,j), i=1..n+1} nondecreasing.

Original entry on oeis.org

22, 105, 567, 3556, 21856, 135636, 836259, 5134856, 31326263, 190404404, 1153108628, 6966626079, 42004555617, 252889763684

Offset: 1

R. H. Hardin, Dec 07 2013

nonn

Column 3 of A233301

			Some solutions for n=5
..1..0..0..0....0..0..0..1....0..1..1..0....0..0..1..0....0..1..1..0
..1..0..0..1....1..0..0..0....0..1..0..1....0..0..0..1....0..1..1..0
..1..1..0..0....0..0..0..1....1..0..0..1....0..0..1..0....1..1..0..0
..1..1..0..0....1..1..0..0....0..1..1..0....0..0..0..1....0..0..1..1
..1..0..1..1....0..0..1..1....0..1..0..1....0..0..0..1....1..0..0..1
..0..1..1..1....0..1..1..1....0..0..1..1....0..1..1..1....0..1..1..1

A233300 Number of (n+1)X(4+1) 0..1 arrays x(i,j) with row sums sum{x(i,j), j=1..4+1} nondecreasing, and column sums sum{i^2*x(i,j), i=1..n+1} nondecreasing.

Original entry on oeis.org

34, 232, 1986, 21957, 239330, 2694620, 30257296, 338790472, 3761876941, 41492573432

Offset: 1

R. H. Hardin, Dec 07 2013

nonn

Column 4 of A233301

			Some solutions for n=5
..0..0..0..0..0....0..0..0..0..0....0..0..1..0..1....0..0..0..1..1
..0..0..1..0..0....0..0..1..1..1....0..0..1..0..1....0..1..1..0..0
..1..0..0..1..1....0..1..0..1..1....1..1..0..0..0....1..0..0..1..0
..1..0..1..0..1....0..1..1..1..1....1..0..1..0..1....0..0..1..1..0
..0..0..1..1..1....1..0..1..1..1....0..0..1..1..1....1..0..0..0..1
..0..1..0..1..1....1..1..1..1..1....0..1..0..1..1....0..1..1..1..1

A233305 Number of (5+1) X (n+1) 0..1 arrays x(i,j) with row sums Sum_{j=1..n+1} x(i,j) nondecreasing, and column sums Sum_{i=1..5+1} i^2*x(i,j) nondecreasing.

Original entry on oeis.org

129, 1739, 21856, 239330, 2353493, 20916337, 170084407, 1276676471, 8918067742, 58369345796, 360074924787, 2104323603081, 11702598417138, 62173159707627

Offset: 1

R. H. Hardin, Dec 07 2013

nonn

Row 5 of A233301.

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

Cf. A233301.

A233306 Number of (6+1)X(n+1) 0..1 arrays x(i,j) with row sums sum{x(i,j), j=1..n+1} nondecreasing, and column sums sum{i^2*x(i,j), i=1..6+1} nondecreasing.

Original entry on oeis.org

258, 5964, 135636, 2694620, 48504411, 789640245, 11764401320, 161499728247, 2058135563687

Offset: 1

R. H. Hardin, Dec 07 2013

nonn

Row 6 of A233301

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

cp's OEIS Frontend

A233302 Number of (2+1) X (n+1) 0..1 arrays x(i,j) with row sums sum{x(i,j), j=1..n+1} nondecreasing, and column sums sum{i^2*x(i,j), i=1..2+1} nondecreasing.

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A233303 Number of (3+1)X(n+1) 0..1 arrays x(i,j) with row sums sum{x(i,j), j=1..n+1} nondecreasing, and column sums sum{i^2*x(i,j), i=1..3+1} nondecreasing.

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A233297 Number of (n+1)X(1+1) 0..1 arrays x(i,j) with row sums sum{x(i,j), j=1..1+1} nondecreasing, and column sums sum{i^2*x(i,j), i=1..n+1} nondecreasing.

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A233304 Number of (4+1) X (n+1) 0..1 arrays x(i,j) with row sums sum{x(i,j), j=1..n+1} nondecreasing, and column sums sum{i^2*x(i,j), i=1..4+1} nondecreasing.

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A233298 Number of (n+1) X (2+1) 0..1 arrays x(i,j) with row sums Sum_{j=1..2+1} x(i,j) nondecreasing, and column sums Sum_{i=1..n+1} i^2*x(i,j) nondecreasing.

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A233299 Number of (n+1)X(3+1) 0..1 arrays x(i,j) with row sums sum{x(i,j), j=1..3+1} nondecreasing, and column sums sum{i^2*x(i,j), i=1..n+1} nondecreasing.

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A233300 Number of (n+1)X(4+1) 0..1 arrays x(i,j) with row sums sum{x(i,j), j=1..4+1} nondecreasing, and column sums sum{i^2*x(i,j), i=1..n+1} nondecreasing.

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A233305 Number of (5+1) X (n+1) 0..1 arrays x(i,j) with row sums Sum_{j=1..n+1} x(i,j) nondecreasing, and column sums Sum_{i=1..5+1} i^2*x(i,j) nondecreasing.

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A233306 Number of (6+1)X(n+1) 0..1 arrays x(i,j) with row sums sum{x(i,j), j=1..n+1} nondecreasing, and column sums sum{i^2*x(i,j), i=1..6+1} nondecreasing.

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