A229774 -id:A229774 - cp's OEIS frontend

A229770 Number of n X n 0..2 arrays with rows in lexicographically nondecreasing order and columns in nonincreasing order.

3, 22, 322, 12958, 2179956, 1976588468, 10811999412826, 378274896023686216, 88035611475274172311886, 140618374201747733896872001960

Offset: 1

R. H. Hardin, Sep 29 2013

nonn

Column 2 of A229774

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

A229771 Number of n X n 0..3 arrays with rows in lexicographically nondecreasing order and columns in nonincreasing order.

Original entry on oeis.org

4, 60, 3232, 1058494, 3062815568, 90462380211862, 29201160476766771330, 108134253835820664368578112

Offset: 1

R. H. Hardin, Sep 29 2013

nonn

Column 3 of A229774

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

A229775 Number of 3 X 3 0..n arrays with rows in lexicographically nondecreasing order and columns in nonincreasing order.

Original entry on oeis.org

20, 322, 3232, 21331, 103222, 397460, 1287672, 3647349, 9281272, 21642038, 46934680, 95749927, 185397226, 343142248, 610590224, 1049496105, 1749325212, 2836933738, 4488787184, 6946186555, 10534026910, 15683670652, 22960578760

Offset: 1

R. H. Hardin, Sep 29 2013

nonn

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

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

Row 3 of A229774.

Empirical: a(n) = (1/120)*n^9 + (1/12)*n^8 + (133/360)*n^7 + (371/360)*n^6 + (19/9)*n^5 + (247/72)*n^4 + (403/90)*n^3 + (401/90)*n^2 + (91/30)*n + 1.
Conjectures from Colin Barker, Sep 21 2018: (Start)
G.f.: x*(20 + 122*x + 912*x^2 + 1101*x^3 + 912*x^4 - 125*x^5 + 118*x^6 - 45*x^7 + 10*x^8 - x^9) / (1 - x)^10.
a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>10.
(End)

A229776 Number of 4X4 0..n arrays with rows in lexicographically nondecreasing order and columns in nonincreasing order.

Original entry on oeis.org

70, 12958, 1058494, 35452250, 637396928, 7379634620, 61734072288, 402537583863, 2155573868470, 9841145888530, 39380724254950, 141067066333648, 459822149867432, 1381730749348760, 3867950992777232, 10173948824534685

Offset: 1

R. H. Hardin, Sep 29 2013

nonn

Row 4 of A229774

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

R. H. Hardin, Table of n, a(n) for n = 1..42

Empirical: a(n) = (1/5040)*n^16 + (17/5040)*n^15 + (89/3360)*n^14 + (143/1120)*n^13 + (307/720)*n^12 + (307/288)*n^11 + (64247/30240)*n^10 + (53933/15120)*n^9 + (10645/2016)*n^8 + (71609/10080)*n^7 + (44/5)*n^6 + (14447/1440)*n^5 + (8975/864)*n^4 + (20359/2160)*n^3 + (3505/504)*n^2 + (1543/420)*n + 1

A229777 Number of 5X5 0..n arrays with rows in lexicographically nondecreasing order and columns in nonincreasing order.

Original entry on oeis.org

252, 2179956, 3062815568, 843211336888, 81937334158292, 3896490956821414, 110102810429666544, 2093314279759590565, 29136130649614970102, 315228320642171324718, 2770642691605055402356, 20456013945849864263232

Offset: 1

R. H. Hardin, Sep 29 2013

nonn

Row 5 of A229774

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

R. H. Hardin, Table of n, a(n) for n = 1..17

A229772 Number of n X n 0..4 arrays with rows in lexicographically nondecreasing order and columns in nonincreasing order.

Original entry on oeis.org

5, 135, 21331, 35452250, 843211336888, 322942973130396495, 2131384087795458774515411

Offset: 1

R. H. Hardin, Sep 29 2013

nonn

Column 4 of A229774

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

A229773 Number of n X n 0..5 arrays with rows in lexicographically nondecreasing order and columns in nonincreasing order.

Original entry on oeis.org

6, 266, 103222, 637396928, 81937334158292, 245200063296427870294, 18316874320807782299001320802

Offset: 1

R. H. Hardin, Sep 29 2013

nonn

Column 5 of A229774

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

A229778 Number of 6X6 0..n arrays with rows in lexicographically nondecreasing order and columns in nonincreasing order.

Original entry on oeis.org

924, 1976588468, 90462380211862, 322942973130396495, 245200063296427870294, 65350451915118676316696, 8161432175844147542615052, 573385480689864447112662651, 25636132281885860529849116700

Offset: 1

R. H. Hardin, Sep 29 2013

nonn

Row 6 of A229774

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

cp's OEIS Frontend

A229770 Number of n X n 0..2 arrays with rows in lexicographically nondecreasing order and columns in nonincreasing order.

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A229771 Number of n X n 0..3 arrays with rows in lexicographically nondecreasing order and columns in nonincreasing order.

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A229775 Number of 3 X 3 0..n arrays with rows in lexicographically nondecreasing order and columns in nonincreasing order.

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A229776 Number of 4X4 0..n arrays with rows in lexicographically nondecreasing order and columns in nonincreasing order.

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A229777 Number of 5X5 0..n arrays with rows in lexicographically nondecreasing order and columns in nonincreasing order.

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A229772 Number of n X n 0..4 arrays with rows in lexicographically nondecreasing order and columns in nonincreasing order.

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A229773 Number of n X n 0..5 arrays with rows in lexicographically nondecreasing order and columns in nonincreasing order.

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Examples

A229778 Number of 6X6 0..n arrays with rows in lexicographically nondecreasing order and columns in nonincreasing order.

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