A223961 -id:A223961 - cp's OEIS frontend

A223957 Number of nX4 0..3 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

35, 805, 12311, 176893, 2575955, 37844037, 559416917, 8299429418, 123370738379, 1835707326614, 27327510542054, 406907786331737, 6059551623581467, 90242115362238750, 1343972755503334184, 20016039213440972353

Offset: 1

R. H. Hardin Mar 29 2013

nonn

Column 4 of A223961

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

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

Empirical: a(n) = 35*a(n-1) -411*a(n-2) +1521*a(n-3) +4495*a(n-4) -33893*a(n-5) -76333*a(n-6) +769422*a(n-7) -657978*a(n-8) -4892638*a(n-9) +11892141*a(n-10) +26545075*a(n-11) -212154687*a(n-12) +180127811*a(n-13) +844199306*a(n-14) -1964869675*a(n-15) -925267902*a(n-16) +18361374116*a(n-17) -28421809002*a(n-18) +14606204778*a(n-19) +43447425250*a(n-20) +45550238994*a(n-21) -206541843216*a(n-22) +420735920152*a(n-23) +123206624124*a(n-24) -263534650788*a(n-25) -263768865528*a(n-26) +1543560996888*a(n-27) +154734998544*a(n-28) -494508716208*a(n-29) -124707094560*a(n-30) +893424774528*a(n-31) +244581703200*a(n-32) +20427292800*a(n-33) +536699520*a(n-34) for n>36

A223956 Number of nX3 0..3 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

Original entry on oeis.org

20, 295, 3471, 41006, 485714, 5777663, 68892600, 822141033, 9813968785, 117159879996, 1398692077165, 16698106010927, 199348287106117, 2379894628461976, 28412070357384947, 339193873130519142

Offset: 1

R. H. Hardin Mar 29 2013

nonn

Column 3 of A223961

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

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

Empirical: a(n) = 20*a(n-1) -105*a(n-2) +51*a(n-3) +589*a(n-4) +1340*a(n-5) -8833*a(n-6) -2855*a(n-7) +30423*a(n-8) +57774*a(n-9) -140760*a(n-10) -176184*a(n-11) +106272*a(n-12) +544320*a(n-13)

A223958 Number of nX5 0..3 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

Original entry on oeis.org

56, 1876, 36028, 594286, 9779558, 163752797, 2772658693, 47273211674, 809416786834, 13894273785956, 238867008057298, 4110191305837227, 70761275087518799, 1218613301433676245, 20990363391641556709

Offset: 1

R. H. Hardin Mar 29 2013

nonn

Column 5 of A223961

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 63

Empirical recurrence of order 63 (see link above)

A223959 Number of nX6 0..3 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

Original entry on oeis.org

84, 3906, 92734, 1718057, 30643468, 556027700, 10269723035, 191829887779, 3609049327918, 68212899813271, 1293084011261962, 24559344963113337, 467028467106529258, 8888318851289202078, 169249293097773923431

Offset: 1

R. H. Hardin Mar 29 2013

nonn

Column 6 of A223961

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

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

A223960 Number of nX7 0..3 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

Original entry on oeis.org

120, 7470, 217144, 4500818, 85350934, 1629022329, 31770135236, 629825651180, 12620835427126, 254719515611821, 5165793380135728, 105110696722615853, 2143594088287821599, 43784293043682987873, 895295525455930993505

Offset: 1

R. H. Hardin Mar 29 2013

nonn

Column 7 of A223961

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

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

A223962 Number of 2 X n 0..3 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

Original entry on oeis.org

16, 85, 295, 805, 1876, 3906, 7470, 13365, 22660, 36751, 57421, 86905, 127960, 183940, 258876, 357561, 485640, 649705, 857395, 1117501, 1440076, 1836550, 2319850, 2904525, 3606876, 4445091, 5439385, 6612145, 7988080, 9594376

Offset: 1

R. H. Hardin, Mar 29 2013

nonn

Row 2 of A223961.

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

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

Cf. A223961.

Empirical: a(n) = (1/144)*n^6 + (7/48)*n^5 + (157/144)*n^4 + (59/16)*n^3 + (425/72)*n^2 + (25/6)*n + 1.
Conjectures from Colin Barker, Aug 24 2018: (Start)
G.f.: x*(16 - 27*x + 36*x^2 - 35*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)

A223963 Number of 3 X n 0..3 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

Original entry on oeis.org

64, 707, 3471, 12311, 36028, 92734, 217144, 471994, 965172, 1874532, 3482781, 6225291, 10754192, 18022648, 29393806, 46779538, 72814768, 111073890, 166336539, 244910775, 355022580, 507281450, 715232788, 996008770, 1371090364

Offset: 1

R. H. Hardin, Mar 29 2013

nonn

Row 3 of A223961.

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

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

Cf. A223961.

Empirical: a(n) = (1/8640)*n^9 + (1/320)*n^8 + (503/10080)*n^7 + (659/1440)*n^6 + (3013/960)*n^5 + (37141/2880)*n^4 + (106019/2160)*n^3 - (18977/720)*n^2 + (2711/70)*n - 6 for n>2.
Conjectures from Colin Barker, Aug 24 2018: (Start)
G.f.: x*(64 + 67*x - 719*x^2 + 1736*x^3 - 2287*x^4 + 2271*x^5 - 2070*x^6 + 1632*x^7 - 910*x^8 + 311*x^9 - 58*x^10 + 5*x^11) / (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>12.
(End)

A223964 Number of 4Xn 0..3 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

Original entry on oeis.org

256, 5864, 41006, 176893, 594286, 1718057, 4500818, 10981150, 25334630, 55772240, 117841845, 239976226, 472531867, 902107834, 1673660678, 3023882381, 5330533450, 9183978785, 15489123731, 25608363453, 41559120445, 66283141375

Offset: 1

R. H. Hardin Mar 29 2013

nonn

Row 4 of A223961

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

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

Empirical: a(n) = (1/1036800)*n^12 + (1/34560)*n^11 + (4379/7257600)*n^10 + (757/80640)*n^9 + (257687/2419200)*n^8 + (82939/80640)*n^7 + (8187071/1036800)*n^6 + (1661651/34560)*n^5 + (117000427/453600)*n^4 + (10787803/20160)*n^3 - (153061829/50400)*n^2 + (3421969/840)*n + 275 for n>5

A223965 Number of 5 X n 0..3 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

Original entry on oeis.org

1024, 48620, 485714, 2575955, 9779558, 30643468, 85350934, 220335341, 539722230, 1270939682, 2897487924, 6419463692, 13849588776, 29130616029, 59785815715, 119811736276, 234625138625, 449330010578, 842238087946, 1546539992378

Offset: 1

R. H. Hardin, Mar 29 2013

nonn

Row 5 of A223961.

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

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

Cf. A223961.

Empirical: a(n) = (1/217728000)*n^15 + (1/7257600)*n^14 + (1021/283046400)*n^13 + (89/1267200)*n^12 + (49747/42768000)*n^11 + (114077/7257600)*n^10 + (4197611/21772800)*n^9 + (2072933/1036800)*n^8 + (4176906623/217728000)*n^7 + (25808249/172800)*n^6 + (198423611/194400)*n^5 + (1908980977/453600)*n^4 + (19380549743/4536000)*n^3 - (3498352713/30800)*n^2 + (12988213717/90090)*n + 329692 for n>8.

A223966 Number of 6Xn 0..3 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

Original entry on oeis.org

4096, 403104, 5777663, 37844037, 163752797, 556027700, 1629022329, 4351046624, 10953882109, 26519610433, 62472567689, 144124515790, 326646013571, 728132468716, 1596498777021, 3441674914130, 7290815852670, 15169818503342

Offset: 1

R. H. Hardin Mar 29 2013

nonn

Row 6 of A223961

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

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

Empirical: a(n) = (1/73156608000)*n^18 + (1/2709504000)*n^17 + (3319/268240896000)*n^16 + (247579/871782912000)*n^15 + (1111849/193729536000)*n^14 + (3684553/35582976000)*n^13 + (658841977/402361344000)*n^12 + (521443357/22353408000)*n^11 + (7665391471/24385536000)*n^10 + (90826901857/24385536000)*n^9 + (333381059779/8128512000)*n^8 + (85061672873/217728000)*n^7 + (319642737999043/100590336000)*n^6 + (118989237432757/5588352000)*n^5 + (107614272658699/1862784000)*n^4 + (891088311042211/9081072000)*n^3 - (51719689062621/11211200)*n^2 + (1774047167507/360360)*n + 34898064 for n>11

cp's OEIS Frontend

A223957 Number of nX4 0..3 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

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A223956 Number of nX3 0..3 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

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A223958 Number of nX5 0..3 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

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A223959 Number of nX6 0..3 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

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A223960 Number of nX7 0..3 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

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A223962 Number of 2 X n 0..3 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

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A223963 Number of 3 X n 0..3 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

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A223964 Number of 4Xn 0..3 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

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A223965 Number of 5 X n 0..3 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

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A223966 Number of 6Xn 0..3 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

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