A224374 -id:A224374 - cp's OEIS frontend

A224368 Number of n X n 0..2 arrays with rows unimodal and antidiagonals nondecreasing.

3, 54, 1838, 77793, 3607078, 174854516, 8684742989, 437757725110, 22283207886650, 1142441203546438, 58904154561219603, 3051594326913582293, 158760240705250821719, 8291742411017787312243, 434658935860309950718887

Offset: 1

R. H. Hardin Apr 05 2013

nonn

Diagonal of A224374

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

R. H. Hardin, Table of n, a(n) for n = 1..24

A224369 Number of n X 3 0..2 arrays with rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

22, 218, 1838, 15540, 132236, 1126072, 9588028, 81634704, 695055928, 5917866680, 50386093544, 428998916880, 3652596505952, 31099055733376, 264784589835472, 2254437550085472, 19194805371407680, 163429034985577568

Offset: 1

R. H. Hardin, Apr 05 2013

nonn

Column 3 of A224374.

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

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

Cf. A224374.

Empirical: a(n) = 10*a(n-1) - 16*a(n-2) + 30*a(n-3) - 14*a(n-4) + 12*a(n-5).

Empirical g.f.: 2*x*(1 + x + x^2)*(11 - 12*x + 6*x^2) / (1 - 10*x + 16*x^2 - 30*x^3 + 14*x^4 - 12*x^5). - Colin Barker, Aug 30 2018

A224370 Number of n X 4 0..2 arrays with rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

46, 698, 7608, 77793, 800309, 8297747, 86251004, 896856330, 9325161494, 96954549463, 1008030060622, 10480399768714, 108963825909899, 1132887953497801, 11778544075116434, 122460568078334321

Offset: 1

R. H. Hardin, Apr 05 2013

nonn

Column 4 of A224374.

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

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

Cf. A224374.

Empirical: a(n) = 15*a(n-1) - 58*a(n-2) + 105*a(n-3) + 20*a(n-4) - 183*a(n-5) + 220*a(n-6) + 240*a(n-7) for n>8.

Empirical g.f.: x*(46 + 8*x - 194*x^2 - 673*x^3 + 468*x^4 + 724*x^5 - 90*x^6 - 45*x^7) / (1 - 15*x + 58*x^2 - 105*x^3 - 20*x^4 + 183*x^5 - 220*x^6 - 240*x^7). - Colin Barker, Aug 30 2018

A224371 Number of nX5 0..2 arrays with rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

86, 1915, 26314, 311367, 3607078, 42132769, 495660330, 5848449149, 69064897862, 815702088065, 9633856474182, 113778532335717, 1343744395119438, 15869813554422065, 187424656004529134, 2213510515188443829

Offset: 1

R. H. Hardin Apr 05 2013

nonn

Column 5 of A224374

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

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

Empirical: a(n) = 21*a(n-1) -141*a(n-2) +427*a(n-3) -546*a(n-4) +526*a(n-5) -2124*a(n-6) +3302*a(n-7) +2396*a(n-8) +7504*a(n-9) +580*a(n-10) +1632*a(n-11) for n>13

A224372 Number of nX6 0..2 arrays with rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

148, 4690, 80819, 1092281, 13831334, 174854516, 2231009824, 28645726612, 368818252942, 4752723627808, 61255849072312, 789494767364269, 10175118017926314, 131136401564099516, 1690070260377561269

Offset: 1

R. H. Hardin Apr 05 2013

nonn

Column 6 of A224374

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

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

Empirical: a(n) = 28*a(n-1) -283*a(n-2) +1386*a(n-3) -3562*a(n-4) +4940*a(n-5) -3840*a(n-6) -14256*a(n-7) +50007*a(n-8) -26386*a(n-9) +141154*a(n-10) +250789*a(n-11) +41356*a(n-12) +274344*a(n-13) +134400*a(n-14) for n>18

A224373 Number of nX7 0..2 arrays with rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

239, 10511, 227112, 3518302, 48166179, 644368221, 8684742989, 118171436342, 1617034882854, 22180823169132, 304470584215636, 4179566726619035, 57366850907237080, 787294489483452053, 10803851806245324942

Offset: 1

R. H. Hardin Apr 05 2013

nonn

Column 7 of A224374

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

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

Empirical: a(n) = 36*a(n-1) -505*a(n-2) +3667*a(n-3) -15271*a(n-4) +38113*a(n-5) -59621*a(n-6) +53813*a(n-7) -125335*a(n-8) +657330*a(n-9) -1326014*a(n-10) +2644047*a(n-11) +3529521*a(n-12) +7803900*a(n-13) +959690*a(n-14) +28175350*a(n-15) +27269532*a(n-16) +18725976*a(n-17) +1826832*a(n-18) +1263744*a(n-19) for n>24

A224375 Number of 3Xn 0..2 arrays with rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

27, 324, 1838, 7608, 26314, 80819, 227112, 593400, 1455898, 3378085, 7455007, 15725041, 31840088, 62123439, 117194882, 214407666, 381424761, 661365902, 1120086056, 1856304530, 3015496746, 4808693047, 7537606592, 11627841824

Offset: 1

R. H. Hardin Apr 05 2013

nonn

Row 3 of A224374

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

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

Empirical: a(n) = (1/19160064)*n^12 + (1/456192)*n^11 + (2287/43545600)*n^10 + (215/290304)*n^9 + (20603/2903040)*n^8 + (923/17920)*n^7 + (14627101/43545600)*n^6 + (400091/207360)*n^5 + (16965289/2177280)*n^4 + (3069023/362880)*n^3 + (13912639/1663200)*n^2 + (21001/3465)*n - 6

A224376 Number of 4 X n 0..2 arrays with rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

81, 1944, 15540, 77793, 311367, 1092281, 3518302, 10643789, 30548895, 83538706, 218139823, 544930741, 1304961768, 3002671615, 6654904188, 14242413828, 29504608642, 59301307852, 115889490174, 220645337145, 410024971049

Offset: 1

R. H. Hardin, Apr 05 2013

nonn

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

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

Row 4 of A224374.

Empirical: a(n) = (1/106748928000)*n^16 + (1/1482624000)*n^15 + (7/266872320)*n^14 + (127/197683200)*n^13 + (315179/28740096000)*n^12 + (24499/177408000)*n^11 + (89507/65318400)*n^10 + (112109/9676800)*n^9 + (68633371/746496000)*n^8 + (11395841/16128000)*n^7 + (6723664007/1437004800)*n^6 + (295741651/13305600)*n^5 + (262119224347/5189184000)*n^4 - (16331232329/1297296000)*n^3 + (12600631/343200)*n^2 + (38790413/360360)*n - 166 for n>2.

A224377 Number of 5Xn 0..2 arrays with rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

243, 11664, 132236, 800309, 3607078, 13831334, 48166179, 158023549, 497580715, 1514359253, 4458436636, 12678906115, 34773215421, 91905020703, 234118674737, 575345712656, 1365918264285, 3137981575530, 6988511558308, 15115188591949

Offset: 1

R. H. Hardin Apr 05 2013

nonn

Row 5 of A224374

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

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

Empirical: a(n) = (1/1379196149760000)*n^20 + (1/12538146816000)*n^19 + (467/101624979456000)*n^18 + (223/1302884352000)*n^17 + (67777/14944849920000)*n^16 + (8993/99632332800)*n^15 + (29436877/20922789888000)*n^14 + (26572241/1494484992000)*n^13 + (439786693/2299207680000)*n^12 + (20411147/10948608000)*n^11 + (8076494051/459841536000)*n^10 + (1128125897/6967296000)*n^9 + (3054806701103/2179457280000)*n^8 + (547815604487/53374464000)*n^7 + (2418856630291/41513472000)*n^6 + (950711499611/4790016000)*n^5 + (286543564329947/1323241920000)*n^4 - (4310267256629/5513508000)*n^3 + (49217261945707/48886437600)*n^2 + (184937368403/116396280)*n - 3058 for n>3

A224378 Number of 6Xn 0..2 arrays with rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

729, 69984, 1126072, 8297747, 42132769, 174854516, 644368221, 2212959866, 7296488462, 23473954511, 74124038709, 229565868000, 694675751863, 2045339262040, 5840640774160, 16145608364197, 43177424328109

Offset: 1

R. H. Hardin Apr 05 2013

nonn

Row 6 of A224374

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

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

Empirical: a(n) = (1/35608838483312640000)*n^24 + (1/228261785149440000)*n^23 + (2993/8515157028618240000)*n^22 + (1189/64508765368320000)*n^21 + (565139/810967336058880000)*n^20 + (50213/2502985605120000)*n^19 + (102275011/224083079700480000)*n^18 + (630450937/74694359900160000)*n^17 + (6860509793/52725430517760000)*n^16 + (7572768857/4393785876480000)*n^15 + (1975549547/96566722560000)*n^14 + (5979889787/26153487360000)*n^13 + (129750858133763/52725430517760000)*n^12 + (8852225741519/337983528960000)*n^11 + (1757155928198569/6590678814720000)*n^10 + (11208897154284701/4393785876480000)*n^9 + (15905213251807771/762187345920000)*n^8 + (60693804091491173/444609285120000)*n^7 + (56813409423945822743/88699552381440000)*n^6 + (45278410760324474101/29566517460480000)*n^5 - (4851359450955021973/4927752910080000)*n^4 - (59510428654061699/5133075948000)*n^3 + (926682017129053/38440617600)*n^2 + (89190882279703/5354228880)*n - 49724 for n>4

cp's OEIS Frontend

A224368 Number of n X n 0..2 arrays with rows unimodal and antidiagonals nondecreasing.

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A224369 Number of n X 3 0..2 arrays with rows unimodal and antidiagonals nondecreasing.

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A224370 Number of n X 4 0..2 arrays with rows unimodal and antidiagonals nondecreasing.

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A224371 Number of nX5 0..2 arrays with rows unimodal and antidiagonals nondecreasing.

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A224372 Number of nX6 0..2 arrays with rows unimodal and antidiagonals nondecreasing.

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A224373 Number of nX7 0..2 arrays with rows unimodal and antidiagonals nondecreasing.

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A224375 Number of 3Xn 0..2 arrays with rows unimodal and antidiagonals nondecreasing.

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A224376 Number of 4 X n 0..2 arrays with rows unimodal and antidiagonals nondecreasing.

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A224377 Number of 5Xn 0..2 arrays with rows unimodal and antidiagonals nondecreasing.

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A224378 Number of 6Xn 0..2 arrays with rows unimodal and antidiagonals nondecreasing.

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