A224310 -id:A224310 - cp's OEIS frontend

A224305 Number of n X 3 0..2 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

22, 218, 1586, 11361, 82700, 615481, 4634768, 35003328, 264487714, 1997888432, 15087449584, 113921725004, 860155842566, 6494472790364, 49035576285772, 370236844834368, 2795429838028120, 21106576528056696, 159362840727871756

Offset: 1

R. H. Hardin Apr 03 2013

nonn

Column 3 of A224310.

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

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

Cf. A224310.

Empirical: a(n) = 10*a(n-1) -16*a(n-2) -24*a(n-3) -44*a(n-4) +728*a(n-5) -678*a(n-6) -722*a(n-7) -860*a(n-8) +9336*a(n-9) -3916*a(n-10) +792*a(n-11) +320*a(n-12) -11936*a(n-13) +2848*a(n-14) +128*a(n-15) +384*a(n-16) +3840*a(n-17).

A224306 Number of nX4 0..2 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

46, 698, 5996, 45453, 345875, 2717759, 22071219, 182843194, 1528645389, 12825738594, 107715455487, 904773390455, 7599493889175, 63827735783412, 536075684379248, 4502373101398007, 37814478865105363, 317596919801312214

Offset: 1

R. H. Hardin Apr 03 2013

nonn

Column 4 of A224310

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

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

Empirical: a(n) = 15*a(n-1) -58*a(n-2) -13*a(n-3) +160*a(n-4) +1879*a(n-5) -7373*a(n-6) +6407*a(n-7) -2233*a(n-8) +11269*a(n-9) -128277*a(n-10) +514460*a(n-11) -559176*a(n-12) +774916*a(n-13) +91024*a(n-14) -426367*a(n-15) -1572540*a(n-16) -2736461*a(n-17) -3322156*a(n-18) -10388293*a(n-19) +187424*a(n-20) -4090338*a(n-21) +4202406*a(n-22) +9112758*a(n-23) +21520552*a(n-24) +26916252*a(n-25) +22991028*a(n-26) +42071688*a(n-27) +28540632*a(n-28) +18156960*a(n-29) +483840*a(n-30) for n>35

A224307 Number of nX5 0..2 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

86, 1915, 20214, 164514, 1258372, 9829605, 80083648, 677557164, 5882182248, 51821072499, 459888653374, 4094603418389, 36504683598749, 325625769512292, 2905345619322972, 25926555852863165, 231390081746732292

Offset: 1

R. H. Hardin Apr 03 2013

nonn

Column 5 of A224310

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 61

Empirical recurrence of order 61 (see link above)

A224308 Number of nX6 0..2 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

148, 4690, 61953, 562760, 4420701, 33934344, 268379906, 2215451575, 19023816444, 168305254414, 1519045558334, 13877824165049, 127654546150864, 1178500994429585, 10900361047173008, 100920807678845030

Offset: 1

R. H. Hardin Apr 03 2013

nonn

Column 6 of A224310

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 88

Empirical recurrence of order 88 (see link above)

A224309 Number of nX7 0..2 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

239, 10511, 174378, 1825800, 15312504, 118317987, 911404794, 7236130163, 59751261572, 512310103541, 4533427479414, 41097427928564, 379017425099579, 3535755438091183, 33225644610034806, 313628721090498518

Offset: 1

R. H. Hardin Apr 03 2013

nonn

Column 7 of A224310

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

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

A224311 Number of 3Xn 0..2 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

27, 324, 1586, 5996, 20214, 61953, 174378, 454832, 1108958, 2547780, 5554847, 11564081, 23107746, 44519456, 83011127, 150287312, 264917825, 455762696, 766835415, 1264104630, 2044874898, 3250558135, 5083853932, 7831604260

Offset: 1

R. H. Hardin Apr 03 2013

nonn

Row 3 of A224310

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

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

Empirical: a(n) = (1/19160064)*n^12 + (1/1064448)*n^11 + (1507/43545600)*n^10 + (73/161280)*n^9 + (23603/2903040)*n^8 + (111/3584)*n^7 + (13023121/43545600)*n^6 + (130093/96768)*n^5 + (5619469/2177280)*n^4 + (54895/2688)*n^3 - (11456441/1663200)*n^2 + (205131/1540)*n - 196 for n>3

A224312 Number of 4Xn 0..2 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

81, 1944, 11361, 45453, 164514, 562760, 1825800, 5585818, 16074063, 43567313, 111632420, 271667665, 630966702, 1405080075, 3012670262, 6242914246, 12544093805, 24510622826, 46689053477, 86888070112, 158272032306

Offset: 1

R. H. Hardin Apr 03 2013

nonn

Row 4 of A224310

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

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

Empirical: a(n) = (1/106748928000)*n^16 + (1/13343616000)*n^15 + (89/9340531200)*n^14 + (5179/37362124800)*n^13 + (126779/28740096000)*n^12 + (103081/1306368000)*n^11 + (18019/13063680)*n^10 - (76841/261273600)*n^9 + (81547771/746496000)*n^8 + (262193969/1306368000)*n^7 - (318727393/1437004800)*n^6 + (10868710291/359251200)*n^5 - (1656836125459/15567552000)*n^4 + (975909282919/1297296000)*n^3 - (26075217263/10810800)*n^2 + (77958821/8190)*n - 17954 for n>6

A224313 Number of 5Xn 0..2 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

243, 11664, 82700, 345875, 1258372, 4420701, 15312504, 51743213, 168153223, 520664883, 1530227559, 4268724974, 11327557052, 28687337144, 69591692782, 162311418316, 365262043261, 795700321817, 1682982694668, 3465433571507

Offset: 1

R. H. Hardin Apr 03 2013

nonn

Row 5 of A224310

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

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

Empirical: a(n) = (1/1379196149760000)*n^20 - (1/137919614976000)*n^19 + (41/33874993152000)*n^18 + (1/426995712000)*n^17 + (88069/104613949440000)*n^16 + (102569/10461394944000)*n^15 + (1648459/2988969984000)*n^14 + (8052547/1494484992000)*n^13 + (615490013/2299207680000)*n^12 - (886807741/229920768000)*n^11 + (219072974333/3218890752000)*n^10 - (466264670551/1609445376000)*n^9 - (4824912304573/2490808320000)*n^8 + (350881754231/4981616640)*n^7 - (289916128775839/373621248000)*n^6 + (131084442677207/20756736000)*n^5 - (232251293325755159/6175128960000)*n^4 + (1510872624234341/8576568000)*n^3 - (2770659376747739/4655851200)*n^2 + (405320158706/285285)*n - 1873744 for n>9

A224314 Number of 6Xn 0..2 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

729, 69984, 615481, 2717759, 9829605, 33934344, 118317987, 416543502, 1454734611, 4952178320, 16233385381, 50895787205, 152210262323, 434202798968, 1183383351150, 3089018682146, 7745205810204, 18709904381707, 43674432900423

Offset: 1

R. H. Hardin Apr 03 2013

nonn

Row 6 of A224310

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

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

Empirical: a(n) = (1/35608838483312640000)*n^24 - (1/989134402314240000)*n^23 + (29/340606281144729600)*n^22 - (53/37347179950080000)*n^21 + (22843/270322445352960000)*n^20 - (9467/35777970708480000)*n^19 + (662659/9959247986688000)*n^18 + (276971/2196892938240000)*n^17 + (3268463573/52725430517760000)*n^16 - (2963663/488198430720000)*n^15 + (9468406841/251073478656000)*n^14 - (84633169147/72425041920000)*n^13 + (487482300065231/17575143505920000)*n^12 - (1486260397277527/4393785876480000)*n^11 + (9918644607332189/5272543051776000)*n^10 + (43388314670213341/2196892938240000)*n^9 - (3089001310329622433/5335311421440000)*n^8 + (16161770203432180709/2000741783040000)*n^7 - (9131503366840338348499/106439462857728000)*n^6 + (11613280481413038257281/14783258730240000)*n^5 - (88365905776581806936999/14783258730240000)*n^4 + (4417617587739169133/127135008000)*n^3 - (377212760667401564861/2698531355520)*n^2 + (557689056867461/1615152)*n - 399418303 for n>12

A224315 Number of 7Xn 0..2 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

2187, 419904, 4634768, 22071219, 80083648, 268379906, 911404794, 3202146197, 11485486125, 41212527412, 145413457614, 498294091308, 1645129036705, 5209884539118, 15798173688229, 45874155195909, 127717720870044

Offset: 1

R. H. Hardin Apr 03 2013

nonn

Row 7 of A224310

			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..0....0..0..1....0..0..0....0..0..1....0..0..0....0..0..2....0..1..1
..0..0..1....0..2..1....0..0..2....0..1..2....1..1..0....0..2..0....2..1..0
..0..2..0....2..2..2....0..2..2....2..2..1....1..0..0....2..2..0....1..0..0
..2..0..0....2..2..2....2..2..0....2..1..1....2..2..0....2..2..1....0..0..0
..1..0..0....2..2..0....2..1..0....2..1..0....2..0..0....2..1..0....1..0..0
..0..2..0....2..2..0....1..2..1....1..1..1....0..2..0....2..2..1....2..2..1

R. H. Hardin, Table of n, a(n) for n = 1..159
R. H. Hardin, Empirical polynomial of degree 28

Empirical polynomial of degree 28 (see link above)

cp's OEIS Frontend

A224305 Number of n X 3 0..2 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A224306 Number of nX4 0..2 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

Views

Author

Keywords

Comments

Examples

Links

Formula

A224307 Number of nX5 0..2 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

Views

Author

Keywords

Comments

Examples

Links

Formula

A224308 Number of nX6 0..2 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

Views

Author

Keywords

Comments

Examples

Links

Formula

A224309 Number of nX7 0..2 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

Views

Author

Keywords

Comments

Examples

Links

A224311 Number of 3Xn 0..2 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

Views

Author

Keywords

Comments

Examples

Links

Formula

A224312 Number of 4Xn 0..2 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

Views

Author

Keywords

Comments

Examples

Links

Formula

A224313 Number of 5Xn 0..2 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

Views

Author

Keywords

Comments

Examples

Links

Formula

A224314 Number of 6Xn 0..2 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

Views

Author

Keywords

Comments

Examples

Links

Formula

A224315 Number of 7Xn 0..2 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

Views

Author

Keywords

Comments

Examples

Links