A223987 -id:A223987 - cp's OEIS frontend

A223981 Number of n X n 0..3 arrays with rows unimodal and columns nondecreasing.

4, 100, 5029, 358118, 31831914, 3322756326, 392525216516, 51162688962195, 7224066705841458, 1089938030989276020, 173886286002145386302, 29095306392044768817550, 5072863442986308208335738

Offset: 1

R. H. Hardin Mar 30 2013

nonn

Diagonal of A223987

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

R. H. Hardin, Table of n, a(n) for n = 1..14

A223982 Number of n X 3 0..3 arrays with rows unimodal and columns nondecreasing.

Original entry on oeis.org

50, 684, 5029, 25410, 99634, 325120, 922768, 2346883, 5462600, 11818092, 24045385, 46430852, 85704412, 152105120, 260790200, 433664645, 701719286, 1107976716, 1711156645, 2590185158, 3849685950, 5626605920, 8098142520, 11491155975

Offset: 1

R. H. Hardin, Mar 30 2013

nonn

Column 3 of A223987.

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

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

Cf. A223987.

Empirical: a(n) = (353/181440)*n^9 + (5/126)*n^8 + (10571/30240)*n^7 + (251/144)*n^6 + (46793/8640)*n^5 + (1565/144)*n^4 + (159679/11340)*n^3 + (715/63)*n^2 + (6491/1260)*n + 1.
Conjectures from Colin Barker, Aug 25 2018: (Start)
G.f.: x*(50 + 184*x + 439*x^2 - 100*x^3 + 259*x^4 - 210*x^5 + 120*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)

A223983 Number of nX4 0..3 arrays with rows unimodal and columns nondecreasing.

Original entry on oeis.org

130, 3526, 44803, 358118, 2086196, 9647292, 37395816, 126087157, 379654704, 1040942916, 2637614941, 6248087300, 13964013792, 29662913488, 60254807616, 117633453657, 221649696158, 404535879938, 717351048575, 1239192239626

Offset: 1

R. H. Hardin Mar 30 2013

nonn

Column 4 of A223987

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

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

Empirical: a(n) = (3551/47900160)*n^12 + (89357/39916800)*n^11 + (132341/4354560)*n^10 + (177787/725760)*n^9 + (1892753/1451520)*n^8 + (5834147/1209600)*n^7 + (11057083/870912)*n^6 + (17370313/725760)*n^5 + (6973385/217728)*n^4 + (26874943/907200)*n^3 + (186503/10395)*n^2 + (8831/1386)*n + 1

A223984 Number of nX5 0..3 arrays with rows unimodal and columns nondecreasing.

Original entry on oeis.org

296, 14751, 308470, 3770722, 31831914, 204647416, 1067023886, 4710529013, 18159308422, 62548820489, 195900273940, 565579629660, 1521723229244, 3849481958400, 9222552207476, 21052791564073, 46024420537228

Offset: 1

R. H. Hardin Mar 30 2013

nonn

Column 5 of A223987

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

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

Empirical: a(n) = (769/444787200)*n^15 + (781507/10897286400)*n^14 + (1419127/1037836800)*n^13 + (108727/6842880)*n^12 + (30122453/239500800)*n^11 + (15632539/21772800)*n^10 + (66446071/21772800)*n^9 + (299560531/30481920)*n^8 + (4868287/201600)*n^7 + (5624957/124416)*n^6 + (7644136631/119750400)*n^5 + (797122847/11975040)*n^4 + (85565105/1729728)*n^3 + (933168347/37837800)*n^2 + (73789/10010)*n + 1

A223985 Number of nX6 0..3 arrays with rows unimodal and columns nondecreasing.

Original entry on oeis.org

610, 52591, 1738756, 31585056, 378122264, 3322756326, 22985966340, 131366850521, 642224541548, 2756467192963, 10596041132366, 37055725164722, 119377525079194, 357900074208050, 1006959166065982, 2677364150668003

Offset: 1

R. H. Hardin Mar 30 2013

nonn

Column 6 of A223987

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

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

Empirical: a(n) = (42587101/1600593426432000)*n^18 + (23341517/16167610368000)*n^17 + (1146376367/31384184832000)*n^16 + (6480623/11321856000)*n^15 + (97670169131/15692092416000)*n^14 + (12419845481/249080832000)*n^13 + (1104278423317/3621252096000)*n^12 + (292799530697/201180672000)*n^11 + (1205682607421/219469824000)*n^10 + (57526246621/3483648000)*n^9 + (95561855720567/2414168064000)*n^8 + (16411079047/217728000)*n^7 + (1328902382698939/11769069312000)*n^6 + (7779741596449/59439744000)*n^5 + (74800773679601/653837184000)*n^4 + (94051748107/1297296000)*n^3 + (483108777911/15437822400)*n^2 + (50380667/6126120)*n + 1

A223986 Number of nX7 0..3 arrays with rows unimodal and columns nondecreasing.

Original entry on oeis.org

1163, 165212, 8350154, 219861244, 3661410444, 43307637038, 392525216516, 2873859236297, 17659521902693, 93729371629362, 439299889862080, 1850116568165210, 7099972695985506, 25111747601307148, 82630828730010090

Offset: 1

R. H. Hardin Mar 30 2013

nonn

Column 7 of A223987

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

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

Empirical: a(n) = (3642102403/12772735542927360000)*n^21 + (1828819507/93573154160640000)*n^20 + (115124770751/182467650613248000)*n^19 + (8318749/652138905600)*n^18 + (446143076989/2462451425280000)*n^17 + (1206525314927/627683696640000)*n^16 + (31263943588093/1977203644416000)*n^15 + (7783056899227/75322043596800)*n^14 + (3079623865184773/5649153269760000)*n^13 + (32370958783969/13795246080000)*n^12 + (120111458340271/14485008384000)*n^11 + (93158829341993/3862668902400)*n^10 + (2280948080961292511/39544072888320000)*n^9 + (371762262630263/3292047360000)*n^8 + (5068740614675741/28245766348800)*n^7 + (34137353132761/149448499200)*n^6 + (11720474642505173/51301071360000)*n^5 + (539294046816389/3087564480000)*n^4 + (12076668593664427/123193822752000)*n^3 + (2595939553/68468400)*n^2 + (104988181/11639628)*n + 1

A223988 Number of 3Xn 0..3 arrays with rows unimodal and columns nondecreasing.

Original entry on oeis.org

20, 400, 5029, 44803, 308470, 1738756, 8350154, 35158856, 132595894, 455284536, 1441678804, 4253578398, 11791889562, 30929283640, 77204065141, 184304047745, 422556706314, 933834642586, 1995549087157, 4134881948947, 8327774224280

Offset: 1

R. H. Hardin Mar 30 2013

nonn

Row 3 of A223987

			Some solutions for n=3
..0..2..2....0..0..3....0..1..1....1..2..0....2..1..1....0..1..0....0..1..1
..0..2..2....0..0..3....1..1..3....1..2..1....2..2..1....1..2..0....1..2..1
..3..2..2....2..3..3....3..3..3....1..2..1....3..3..2....3..2..2....1..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 + (2915977/5230697472000)*n^14 + (6071381/747242496000)*n^13 + (748919/8211456000)*n^12 + (23111713/28740096000)*n^11 + (409218107/73156608000)*n^10 + (320706361/10450944000)*n^9 + (107018740483/804722688000)*n^8 + (467745209/1026432000)*n^7 + (10942630223/8895744000)*n^6 + (239853259979/93405312000)*n^5 + (882554800469/217945728000)*n^4 + (6093492161/1297296000)*n^3 + (4200944633/1029188160)*n^2 + (1784593/1021020)*n + 1

A223989 Number of 4Xn 0..3 arrays with rows unimodal and columns nondecreasing.

Original entry on oeis.org

35, 1225, 25410, 358118, 3770722, 31585056, 219861244, 1312747586, 6885325482, 32313530946, 137690265950, 539018300034, 1957451099304, 6647631120056, 21256016741041, 64364748455011, 185491652223781, 510953158157281

Offset: 1

R. H. Hardin Mar 30 2013

nonn

Row 4 of A223987

			Some solutions for n=3
..0..0..0....0..1..0....1..1..2....0..2..1....0..0..0....1..2..0....0..2..0
..1..1..1....0..1..0....1..3..3....0..2..2....2..3..1....2..3..1....0..2..1
..1..3..3....0..2..0....2..3..3....0..3..2....2..3..1....2..3..1....0..2..1
..1..3..3....0..3..2....2..3..3....3..3..3....3..3..2....3..3..1....0..3..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 + (973813/198604245565440000)*n^20 + (4751599/38617492193280000)*n^19 + (31125329/12804747411456000)*n^18 + (103519301/2667655710720000)*n^17 + (2190105457/4304116776960000)*n^16 + (4631351591/836911595520000)*n^15 + (151304213363/3012881743872000)*n^14 + (22821847439/59779399680000)*n^13 + (807436276336499/331416991825920000)*n^12 + (2978829718733/228248616960000)*n^11 + (12597307863407/215205838848000)*n^10 + (15260090056063/69742632960000)*n^9 + (21685072444447303/32011868528640000)*n^8 + (72957402495727/42343741440000)*n^7 + (108238697285043737/30411275102208000)*n^6 + (24731243901001117/4223788208640000)*n^5 + (1127736066113539/150849578880000)*n^4 + (8436170802181/1173274502400)*n^3 + (193928573189123/37104806138400)*n^2 + (1070454625/535422888)*n + 1

A223990 Number of 5Xn 0..3 arrays with rows unimodal and columns nondecreasing.

Original entry on oeis.org

56, 3136, 99634, 2086196, 31831914, 378122264, 3661410444, 29889154034, 211009204916, 1314178222276, 7336228725354, 37185201981670, 172974779780114, 745060738789758, 2994209711354545, 11299608627412727, 40267814207071512

Offset: 1

R. H. Hardin Mar 30 2013

nonn

Row 5 of A223987

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

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)

A223991 Number of 6Xn 0..3 arrays with rows unimodal and columns nondecreasing.

Original entry on oeis.org

84, 7056, 325120, 9647292, 204647416, 3322756326, 43307637038, 469239396496, 4340915844892, 35013234463686, 250416999823220, 1610131956940138, 9414450936518133, 50540930874984955, 251164546472066722

Offset: 1

R. H. Hardin Mar 30 2013

nonn

Row 6 of A223987

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

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

Empirical polynomial of degree 36 (see link above)

cp's OEIS Frontend

A223981 Number of n X n 0..3 arrays with rows unimodal and columns nondecreasing.

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A223982 Number of n X 3 0..3 arrays with rows unimodal and columns nondecreasing.

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A223983 Number of nX4 0..3 arrays with rows unimodal and columns nondecreasing.

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A223984 Number of nX5 0..3 arrays with rows unimodal and columns nondecreasing.

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A223985 Number of nX6 0..3 arrays with rows unimodal and columns nondecreasing.

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A223986 Number of nX7 0..3 arrays with rows unimodal and columns nondecreasing.

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A223988 Number of 3Xn 0..3 arrays with rows unimodal and columns nondecreasing.

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A223989 Number of 4Xn 0..3 arrays with rows unimodal and columns nondecreasing.

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A223990 Number of 5Xn 0..3 arrays with rows unimodal and columns nondecreasing.

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A223991 Number of 6Xn 0..3 arrays with rows unimodal and columns nondecreasing.

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