A224204 -id:A224204 - cp's OEIS frontend

A224198 Number of n X n 0..3 arrays with rows unimodal and antidiagonals nondecreasing.

4, 160, 16060, 2411246, 451319098, 96914926654, 22835261226043, 5750097317505437, 1521786116504544601, 418628292901694453231, 118789461093773656747975, 34580941641153629118242103

Offset: 1

R. H. Hardin, Apr 01 2013

nonn

Diagonal of A224204.

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

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

Cf. A224204.

A224199 Number of nX3 0..3 arrays with rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

50, 984, 16060, 263516, 4357084, 72105068, 1193130640, 19742052632, 326659600368, 5405039750704, 89433956076272, 1479810123371280, 24485531969701600, 405147434704078656, 6703731985610244736

Offset: 1

R. H. Hardin Apr 01 2013

nonn

Column 3 of A224204

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

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

Empirical: a(n) = 20*a(n-1) -70*a(n-2) +228*a(n-3) -276*a(n-4) +392*a(n-5) -196*a(n-6) +144*a(n-7)

A224200 Number of nX4 0..3 arrays with rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

130, 4580, 108625, 2411246, 54177872, 1229044416, 27957232796, 636184842092, 14476260508500, 329391607167600, 7494853316529036, 170534677669656388, 3880272541450452972, 88290059453259690888, 2008914306032132754800

Offset: 1

R. H. Hardin Apr 01 2013

nonn

Column 4 of A224204

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

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

Empirical: a(n) = 35*a(n-1) -347*a(n-2) +1689*a(n-3) -2986*a(n-4) -2311*a(n-5) +23532*a(n-6) -23864*a(n-7) -36468*a(n-8) +100464*a(n-9) +94080*a(n-10) for n>12

A224201 Number of nX5 0..3 arrays with rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

296, 17723, 586343, 16355242, 451319098, 12652618110, 357890479324, 10153767871028, 288290902851198, 8186391229197618, 232464667737624940, 6601126525130276106, 187446397143433832288, 5322740642815551322518

Offset: 1

R. H. Hardin Apr 01 2013

nonn

Column 5 of A224204

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

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

Empirical: a(n) = 56*a(n-1) -1098*a(n-2) +10776*a(n-3) -59038*a(n-4) +197135*a(n-5) -527776*a(n-6) +1780117*a(n-7) -5020078*a(n-8) +3603978*a(n-9) -19091082*a(n-10) +61460622*a(n-11) +49090018*a(n-12) +274177128*a(n-13) +105163104*a(n-14) +354022404*a(n-15) +28705280*a(n-16) +147891456*a(n-17) -1275168*a(n-18) +15980544*a(n-19) for n>23

A224202 Number of nX6 0..3 arrays with rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

610, 59792, 2734683, 93052770, 2981774784, 96914926654, 3202561268692, 106630751360602, 3558964686578544, 118857103988506092, 3969834734632962762, 132593577206338949766, 4428640833523450577612, 147916669230853276174408

Offset: 1

R. H. Hardin Apr 01 2013

nonn

Column 6 of A224204

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

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

Empirical: a(n) = 84*a(n-1) -2771*a(n-2) +49004*a(n-3) -526214*a(n-4) +3641009*a(n-5) -16632719*a(n-6) +48536326*a(n-7) -53423733*a(n-8) -313959977*a(n-9) +1729942603*a(n-10) -7086418537*a(n-11) +13780962535*a(n-12) +5231265096*a(n-13) -20279410782*a(n-14) +609579098232*a(n-15) +294855159788*a(n-16) +2331852968592*a(n-17) +7276333185488*a(n-18) +4826951354776*a(n-19) +18771064269632*a(n-20) +25683656373760*a(n-21) +16941876341184*a(n-22) +25615354625280*a(n-23) +22113238049280*a(n-24) +5504163840000*a(n-25) for n>32

A224203 Number of nX7 0..3 arrays with rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

1163, 180821, 11446096, 475218035, 17178450136, 618703866073, 22835261226043, 856178295327574, 32299825618280351, 1220504574023229563, 46124705848425800316, 1742806875797016046956, 65840694352751999751002

Offset: 1

R. H. Hardin Apr 01 2013

nonn

Column 7 of A224204

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 41

Empirical recurrence of order 41 (see link above)

A224205 Number of 3Xn 0..3 arrays with rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

64, 1600, 16060, 108625, 586343, 2734683, 11446096, 43787371, 154644169, 507763502, 1559390798, 4504599056, 12304311893, 31936080080, 79116405604, 187828358540, 428877669532, 944895859570, 2014476071694, 4166609485641

Offset: 1

R. H. Hardin Apr 01 2013

nonn

Row 3 of A224204

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

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

Empirical: a(n) = (1/3629463552000)*n^18 + (1/44808192000)*n^17 + (10403/10461394944000)*n^16 + (10537/373621248000)*n^15 + (2917237/5230697472000)*n^14 + (6087761/747242496000)*n^13 + (5301533/57480192000)*n^12 + (3437329/4105728000)*n^11 + (464094467/73156608000)*n^10 + (442073521/10450944000)*n^9 + (211531872283/804722688000)*n^8 + (20899761511/14370048000)*n^7 + (120074702257/20756736000)*n^6 + (177621646127/13343616000)*n^5 + (1548685310923/72648576000)*n^4 + (22497639401/1297296000)*n^3 + (9654394423/1715313600)*n^2 + (19245361/1021020)*n - 20

A224206 Number of 4Xn 0..3 arrays with rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

256, 16000, 263516, 2411246, 16355242, 93052770, 475218035, 2252100875, 10026501335, 42033573628, 165872759545, 616278459399, 2159074455116, 7151151269790, 22464417502819, 67161353094487, 191751351630146

Offset: 1

R. H. Hardin Apr 01 2013

nonn

Row 4 of A224204

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

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

Empirical: a(n) = (1/2906843957821440000)*n^24 + (11/242236996485120000)*n^23 + (4897/1529252690853888000)*n^22 + (2857/19308746096640000)*n^21 + (973909/198604245565440000)*n^20 + (93229/757205729280000)*n^19 + (266789/109442285568000)*n^18 + (104478641/2667655710720000)*n^17 + (1429093157/2738983403520000)*n^16 + (4913895191/836911595520000)*n^15 + (171672001139/3012881743872000)*n^14 + (29350223359/59779399680000)*n^13 + (433008014137969/110472330608640000)*n^12 + (76105242218503/2510734786560000)*n^11 + (344040677347481/1506440871936000)*n^10 + (4054053159749/2583060480000)*n^9 + (276889384664596819/32011868528640000)*n^8 + (4163175202299941/127031224320000)*n^7 + (2967972507533347/42533251891200)*n^6 + (338490515487987437/4223788208640000)*n^5 + (85995749191634941/527973526080000)*n^4 - (9502462212673/345080736000)*n^3 - (23527482078379273/74209612276800)*n^2 + (572648006969/535422888)*n - 1055 for n>2

A224207 Number of 5Xn 0..3 arrays with rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

1024, 160000, 4357084, 54177872, 451319098, 2981774784, 17178450136, 91585310015, 466549088803, 2294426837986, 10864811370660, 49206477503159, 211954893113813, 865842155983471, 3352909875833504, 12323194613924281

Offset: 1

R. H. Hardin Apr 01 2013

nonn

Row 5 of A224204

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical polynomial of degree 30

Empirical polynomial of degree 30 (see link above)

A224208 Number of 6 X n 0..3 arrays with rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

4096, 1600000, 72105068, 1229044416, 12652618110, 96914926654, 618703866073, 3548209715979, 19271137728483, 102347986047920, 537384393939360, 2776104877172612, 13950578706978266, 67469676772365413, 311817626166418846

Offset: 1

R. H. Hardin, Apr 01 2013

nonn

Row 6 of A224204.

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical polynomial of degree 36

Cf. A224204.

Empirical polynomial of degree 36 (see link above).

cp's OEIS Frontend

A224198 Number of n X n 0..3 arrays with rows unimodal and antidiagonals nondecreasing.

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A224199 Number of nX3 0..3 arrays with rows unimodal and antidiagonals nondecreasing.

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A224200 Number of nX4 0..3 arrays with rows unimodal and antidiagonals nondecreasing.

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A224201 Number of nX5 0..3 arrays with rows unimodal and antidiagonals nondecreasing.

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A224202 Number of nX6 0..3 arrays with rows unimodal and antidiagonals nondecreasing.

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A224203 Number of nX7 0..3 arrays with rows unimodal and antidiagonals nondecreasing.

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A224205 Number of 3Xn 0..3 arrays with rows unimodal and antidiagonals nondecreasing.

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A224206 Number of 4Xn 0..3 arrays with rows unimodal and antidiagonals nondecreasing.

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A224207 Number of 5Xn 0..3 arrays with rows unimodal and antidiagonals nondecreasing.

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A224208 Number of 6 X n 0..3 arrays with rows unimodal and antidiagonals nondecreasing.

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