A224391 -id:A224391 - cp's OEIS frontend

A224386 Number of nX3 0..3 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

20, 400, 6094, 86701, 1268572, 18794636, 279128617, 4142692993, 61481903024, 912523782542, 13544525098266, 201041292342421, 2984053971336637, 44292278131103241, 657430060365000621, 9758232360460992934

Offset: 1

R. H. Hardin Apr 05 2013

nonn

Column 3 of A224391

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

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

Empirical: a(n) = 20*a(n-1) -70*a(n-2) -211*a(n-3) +2453*a(n-4) -12192*a(n-5) +5907*a(n-6) +119292*a(n-7) -294992*a(n-8) +742820*a(n-9) +144828*a(n-10) -5072952*a(n-11) +6034728*a(n-12) -15994872*a(n-13) -858096*a(n-14) -10368*a(n-15)

A224387 Number of nX4 0..3 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

Original entry on oeis.org

35, 1225, 27790, 497958, 8573507, 152271025, 2780848289, 51325449985, 949582166068, 17572045403455, 325249748226217, 6022221071267123, 111533443784218247, 2065901802649317374, 38268294526698715055

Offset: 1

R. H. Hardin Apr 05 2013

nonn

Column 4 of A224391

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 47

Empirical recurrence of order 47 (see link above)

A224388 Number of nX5 0..3 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

Original entry on oeis.org

56, 3136, 102232, 2332222, 45648753, 879830242, 17642791909, 365858453951, 7713944320142, 163629606236587, 3477919119488292, 73997041686359692, 1575770012461089025, 33581433844112168010, 716050604542387047024

Offset: 1

R. H. Hardin Apr 05 2013

nonn

Column 5 of A224391

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

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

A224389 Number of nX6 0..3 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

Original entry on oeis.org

84, 7056, 319769, 9331553, 211856287, 4364554008, 90682660877, 1970202629627, 44404431681110, 1020688669518185, 23669944875525397, 551060981056174321, 12857376512847673306, 300489121615902701612, 7032615140846782176382

Offset: 1

R. H. Hardin Apr 05 2013

nonn

Column 6 of A224391

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

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

A224390 Number of nX7 0..3 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

Original entry on oeis.org

120, 14400, 881519, 32806574, 882833522, 19879000458, 424124440444, 9276284077351, 212972822153405, 5078434646430668, 123731812099601647, 3047111408129189213, 75453561534676485695, 1874665689163421824860

Offset: 1

R. H. Hardin Apr 05 2013

nonn

Column 7 of A224391

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

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

A224392 Number of 3 X n 0..3 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

Original entry on oeis.org

64, 1000, 6094, 27790, 102232, 319769, 881519, 2196522, 5038720, 10788462, 21789398, 41858498, 76994510, 136338455, 233448747, 387963222, 627730762, 991506308, 1532314870, 2321602662, 3454306716, 5054988261, 7285189791

Offset: 1

R. H. Hardin, Apr 05 2013

nonn

Row 3 of A224391.

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

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

Cf. A224391.

Empirical: a(n) = (353/181440)*n^9 + (17/560)*n^8 + (9731/30240)*n^7 + (1283/720)*n^6 + (52457/8640)*n^5 + (776/45)*n^4 + (294499/11340)*n^3 + (28837/2520)*n^2 + (8207/126)*n - 18 for n>1.
Conjectures from Colin Barker, Aug 30 2018: (Start)
G.f.: x*(64 + 360*x - 1026*x^2 + 4170*x^3 - 7998*x^4 + 10591*x^5 - 9351*x^6 + 5629*x^7 - 2165*x^8 + 478*x^9 - 46*x^10) / (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>11.
(End)

A224393 Number of 4Xn 0..3 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

Original entry on oeis.org

256, 10000, 86701, 497958, 2332222, 9331553, 32806574, 103452812, 297410156, 789731500, 1957606141, 4569537752, 10116846904, 21372349639, 43300242010, 84493906854, 159387825448, 291579791772, 518714491591, 899524090772

Offset: 1

R. H. Hardin Apr 05 2013

nonn

Row 4 of A224391

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

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

Empirical: a(n) = (3551/47900160)*n^12 + (17561/13305600)*n^11 + (410317/21772800)*n^10 + (127787/725760)*n^9 + (394837/290304)*n^8 + (4724393/1209600)*n^7 + (880093831/21772800)*n^6 - (673403/80640)*n^5 + (476636641/1088640)*n^4 + (58121267/907200)*n^3 - (1924453/415800)*n^2 - (1998055/2772)*n + 1906 for n>4

A224394 Number of 5Xn 0..3 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

Original entry on oeis.org

1024, 100000, 1268572, 8573507, 45648753, 211856287, 882833522, 3343528551, 11604617405, 37199618077, 110964317169, 310166468938, 817551602005, 2043560704475, 4868244723248, 11101332102787, 24326305539913

Offset: 1

R. H. Hardin Apr 05 2013

nonn

Row 5 of A224391

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

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

Empirical: a(n) = (769/444787200)*n^15 + (348923/10897286400)*n^14 + (1834741/3113510400)*n^13 + (1653961/239500800)*n^12 + (15881209/239500800)*n^11 + (3185767/4354560)*n^10 + (6331231/21772800)*n^9 + (8051546371/152409600)*n^8 - (92949613/680400)*n^7 + (29776075747/21772800)*n^6 - (235108166129/119750400)*n^5 + (1142919607439/59875200)*n^4 - (2395878032771/43243200)*n^3 + (4577919285997/37837800)*n^2 - (3999067013/10010)*n + 824171 for n>7

A224395 Number of 6Xn 0..3 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

Original entry on oeis.org

4096, 1000000, 18794636, 152271025, 879830242, 4364554008, 19879000458, 84675848787, 337896379016, 1262027034092, 4414609771988, 14497401758306, 44849313719663, 131213360082438, 364483316826362, 964981060109623

Offset: 1

R. H. Hardin Apr 05 2013

nonn

Row 6 of A224391

			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..2....0..0..2....0..0..2....0..0..0....0..0..2....0..0..2
..0..2..3....0..2..2....2..2..3....0..2..2....2..2..2....2..2..2....0..2..2
..0..3..3....0..2..3....0..2..3....2..2..2....0..2..2....2..2..3....0..2..3
..1..2..3....0..0..1....0..1..1....0..2..3....1..3..3....2..2..3....3..3..3
..1..3..3....0..0..2....0..2..3....0..0..1....0..1..1....0..0..1....0..2..2

R. H. Hardin, Table of n, a(n) for n = 1..96

Empirical: a(n) = (42587101/1600593426432000)*n^18 + (83940121/177843714048000)*n^17 + (351548291/31384184832000)*n^16 + (404522743/2615348736000)*n^15 + (2603179801/1426553856000)*n^14 + (13975516589/747242496000)*n^13 + (1018677008761/3621252096000)*n^12 - (71772294491/67060224000)*n^11 + (9590385658061/219469824000)*n^10 - (19294207174217/73156608000)*n^9 + (6061000683461531/2414168064000)*n^8 - (67636294337629/7185024000)*n^7 + (580563104944166119/11769069312000)*n^6 + (14843452118300317/653837184000)*n^5 - (42702408306785177/59439744000)*n^4 + (14422633437701933/3027024000)*n^3 - (272645035897423741/15437822400)*n^2 + (10375478018905/1225224)*n + 82732433 for n>10

A224396 Number of 7Xn 0..3 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

Original entry on oeis.org

16384, 10000000, 279128617, 2780848289, 17642791909, 90682660877, 424124440444, 1895527656502, 8186764103582, 33998418651060, 134714450368164, 506671733476920, 1805110329656189, 6093246282673576, 19519515186829602

Offset: 1

R. H. Hardin Apr 05 2013

nonn

Row 7 of A224391

			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..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0
..0..0..0....0..0..1....0..0..2....0..0..2....0..0..2....0..0..0....0..0..2
..0..2..2....2..2..2....2..2..3....0..2..3....0..0..3....0..0..0....2..2..2
..0..1..1....0..2..2....0..2..2....0..0..0....0..3..3....0..1..1....0..3..3
..1..2..2....2..3..3....2..3..3....0..2..2....0..2..2....1..2..3....2..2..2
..0..1..2....0..2..3....0..3..3....0..0..3....0..1..3....1..2..3....0..1..1

R. H. Hardin, Table of n, a(n) for n = 1..23

cp's OEIS Frontend

A224386 Number of nX3 0..3 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

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A224387 Number of nX4 0..3 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

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A224388 Number of nX5 0..3 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

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A224389 Number of nX6 0..3 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

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A224390 Number of nX7 0..3 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

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A224392 Number of 3 X n 0..3 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

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A224393 Number of 4Xn 0..3 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

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A224394 Number of 5Xn 0..3 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

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A224395 Number of 6Xn 0..3 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

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A224396 Number of 7Xn 0..3 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

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