A213962 -id:A213962 - cp's OEIS frontend

A213963 Number of 3X3 0..n matrices with row and column 1..3 having sum <= i*n.

138, 3186, 32060, 199735, 909900, 3323712, 10301232, 28115505, 69342790, 157454154, 333771516, 667605263, 1270560760, 2316187440, 4066346688, 6905893425, 11387501154, 18288711250, 28683554460, 44031375927, 66285794564

Offset: 1

R. H. Hardin Jun 28 2012

nonn

Row 3 of A213962

			Some solutions for n=4
..2..0..0....4..0..0....4..0..0....2..0..0....0..3..0....2..2..0....1..3..0
..0..0..0....0..1..2....0..2..4....0..2..2....2..1..2....2..2..2....1..4..2
..1..4..2....0..0..1....0..3..3....0..3..1....2..4..0....0..4..3....0..1..0

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

Empirical: a(n) = (n+3) *(n+2) *(449*n^5+3038*n^4+7759*n^3+9790*n^2+6264*n+1680) *(1+n)^2/10080.

A213964 Number of 4X4 0..n matrices with row and column 1..4 having sum <= i*n.

Original entry on oeis.org

5314, 1299735, 74323976, 1839121115, 26346319032, 256652587891, 1876235252048, 10982618599248, 53844488576650, 228411366730514, 858979624713168, 2917594805354242, 9082065855050720, 26213547883869330, 70820298142121408

Offset: 1

R. H. Hardin Jun 28 2012

nonn

Row 4 of A213962

			Some solutions for n=4
..3..0..1..0....1..3..0..0....3..0..0..0....1..3..0..0....4..0..0..0
..1..2..0..3....0..4..2..1....0..4..3..0....3..4..0..0....0..4..0..4
..0..3..1..2....0..1..0..1....0..3..1..4....0..1..3..3....0..1..2..4
..0..2..1..0....1..0..4..0....0..0..0..4....0..0..4..4....0..1..2..4

R. H. Hardin, Table of n, a(n) for n = 1..41

Empirical: a(n) = (4679471/2270268000)*n^16 + (135958687/2476656000)*n^15 + (2078860429/3113510400)*n^14 + (2558219003/518918400)*n^13 + (274698527/11088000)*n^12 + (481269659/5346000)*n^11 + (18685736999/76204800)*n^10 + (19501561159/38102400)*n^9 + (22571956991/27216000)*n^8 + (1057766063/1008000)*n^7 + (82705488571/79833600)*n^6 + (1231373209/1555200)*n^5 + (3137244260567/6810804000)*n^4 + (299434637471/1513512000)*n^3 + (51361787/864864)*n^2 + (268615/24024)*n + 1

A213965 Number of 5 X 5 0..n matrices with row and column 1..5 having sum <= i*n.

Original entry on oeis.org

575122, 2860343784, 1494988224948, 214090209950060, 13186531254708756, 447939229940051654, 9770128253650761936, 151215265523724909552, 1780021685666973242600, 16755629964660417264599, 130936901790313197125592

Offset: 1

R. H. Hardin, Jun 28 2012

nonn

Row 5 of A213962.

			Some solutions for n=4
..2..0..1..0..0....3..0..0..0..0....4..0..0..0..0....0..4..0..0..0
..0..3..1..0..3....0..2..1..4..1....0..4..4..0..0....2..0..1..4..0
..0..3..4..0..3....0..3..0..0..1....0..4..3..0..0....0..1..2..0..0
..2..2..1..2..2....0..2..3..2..3....0..0..3..3..4....0..2..1..3..4
..0..0..4..4..4....0..0..0..2..0....0..0..0..1..4....0..0..4..2..1

R. H. Hardin, Table of n, a(n) for n = 1..15

Cf. A213962.

A213955 Number of n X n 0..1 matrices with row and column i=1..n having sum <= i.

Original entry on oeis.org

2, 10, 138, 5314, 575122, 176041978, 153143689594, 380082566144530, 2699632942815871042, 55016905649245690586122, 3223966155402204759824471786

Offset: 1

R. H. Hardin, Jun 28 2012

nonn

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

Column 1 of A213962.

A213956 Number of n X n 0..2 matrices with row and column i=1..n having sum <= i*2.

Original entry on oeis.org

3, 42, 3186, 1299735, 2860343784, 34107691901433, 2211749000480369037, 782349734245964422491828

Offset: 1

R. H. Hardin Jun 28 2012

nonn

Column 2 of A213962

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

A213957 Number of n X n 0..3 matrices with row and column i=1..n having sum <= i*3.

Original entry on oeis.org

4, 120, 32060, 74323976, 1494988224948, 261421322089741976, 398278555474658144086480, 5298226825488439815883527067288

Offset: 1

R. H. Hardin Jun 28 2012

nonn

Column 3 of A213962

			Some solutions for n=4
..0..0..1..2....1..0..0..0....3..0..0..0....3..0..0..0....3..0..0..0
..0..3..3..0....0..3..1..2....0..1..1..1....0..3..3..0....0..2..2..0
..1..0..1..2....1..0..1..3....0..1..2..3....0..1..3..3....0..3..1..3
..1..1..0..0....1..3..3..1....0..1..2..0....0..1..1..1....0..0..3..3

A213958 Number of n X n 0..4 matrices with row and column i=1..n having sum <= i*4.

Original entry on oeis.org

5, 275, 199735, 1839121115, 214090209950060, 314911377440218697950, 5858129386840205449108592935

Offset: 1

R. H. Hardin Jun 28 2012

nonn

Column 4 of A213962

			Some solutions for n=4
..2..0..2..0....2..0..0..0....1..3..0..0....3..0..0..0....2..1..0..1
..1..3..4..0....2..2..3..0....0..4..2..1....0..4..1..3....0..1..4..1
..0..1..0..3....0..2..2..3....0..1..0..1....0..2..1..1....0..4..3..4
..0..3..4..0....0..2..2..0....1..0..4..0....0..2..4..2....0..0..1..0

A213959 Number of n X n 0..5 matrices with row and column i=1..n having sum <= i*5.

Original entry on oeis.org

6, 546, 909900, 26346319032, 13186531254708756, 113762889909962601897876

Offset: 1

R. H. Hardin Jun 28 2012

nonn

Column 5 of A213962

			Some solutions for n=4
..4..0..0..0....3..0..0..0....4..0..0..0....3..0..2..0....3..0..0..2
..0..3..3..0....0..4..5..0....0..2..5..2....1..0..3..3....2..5..0..2
..0..4..3..0....0..5..5..3....1..5..4..4....0..2..4..5....0..0..1..2
..0..3..0..0....0..0..1..5....0..0..4..4....0..0..2..3....0..5..4..0

A213960 Number of n X n 0..6 matrices with row and column i=1..n having sum <= i*6.

Original entry on oeis.org

7, 980, 3323712, 256652587891, 447939229940051654, 17583943206407091985366455

Offset: 1

R. H. Hardin, Jun 28 2012

nonn

Column 6 of A213962.

			Some solutions for n=4
..0..2..3..0....1..2..0..0....2..3..0..0....1..1..3..0....5..0..0..1
..0..5..5..0....1..4..0..1....0..3..1..5....1..1..6..0....1..0..1..4
..5..0..3..6....1..5..3..3....0..3..4..4....4..4..1..0....0..1..3..4
..0..0..4..5....0..0..1..0....3..0..4..1....0..5..2..5....0..4..6..6

Cf. A213962.

A213961 Number of n X n 0..7 matrices with row and column i=1..n having sum <= i*7.

Original entry on oeis.org

8, 1632, 10301232, 1876235252048, 9770128253650761936, 1444750727564469383124521648

Offset: 1

R. H. Hardin Jun 28 2012

nonn

Column 7 of A213962

			Some solutions for n=4
..1..0..2..0....7..0..0..0....3..0..1..0....1..5..1..0....0..4..1..2
..0..5..0..2....0..7..7..0....4..1..0..0....3..7..2..0....0..3..3..4
..2..5..4..3....0..5..7..7....0..0..7..0....0..2..1..1....5..0..5..2
..0..4..1..4....0..1..1..1....0..1..2..4....3..0..4..4....1..5..0..0

cp's OEIS Frontend

A213963 Number of 3X3 0..n matrices with row and column 1..3 having sum <= i*n.

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A213964 Number of 4X4 0..n matrices with row and column 1..4 having sum <= i*n.

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A213965 Number of 5 X 5 0..n matrices with row and column 1..5 having sum <= i*n.

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A213955 Number of n X n 0..1 matrices with row and column i=1..n having sum <= i.

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A213956 Number of n X n 0..2 matrices with row and column i=1..n having sum <= i*2.

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A213957 Number of n X n 0..3 matrices with row and column i=1..n having sum <= i*3.

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A213958 Number of n X n 0..4 matrices with row and column i=1..n having sum <= i*4.

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A213959 Number of n X n 0..5 matrices with row and column i=1..n having sum <= i*5.

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A213960 Number of n X n 0..6 matrices with row and column i=1..n having sum <= i*6.

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A213961 Number of n X n 0..7 matrices with row and column i=1..n having sum <= i*7.

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