A224353 -id:A224353 - cp's OEIS frontend

A224348 Number of nX3 0..2 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

10, 100, 788, 5880, 45064, 349280, 2710892, 21021916, 163012744, 1264202660, 9804721360, 76042111360, 589756075600, 4573942739248, 35473931052816, 275123688202096, 2133765358334352, 16548755248130912, 128346493442546640

Offset: 1

R. H. Hardin Apr 04 2013

nonn

Column 3 of A224353

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

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

Empirical: a(n) = 10*a(n-1) -16*a(n-2) -24*a(n-3) +164*a(n-4) -516*a(n-5) +140*a(n-6) +956*a(n-7) -1500*a(n-8) +3180*a(n-9) +60*a(n-10)

A224349 Number of n X 4 0..2 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

Original entry on oeis.org

15, 225, 2321, 19608, 160362, 1351748, 11704964, 102319662, 895494806, 7833508842, 68530349850, 599768316699, 5250822841015, 45977188883801, 402610713736831, 3525653178203557, 30874547729660838, 270374890703092436

Offset: 1

R. H. Hardin, Apr 04 2013

nonn

Column 4 of A224353.

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

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

Cf. A224353.

Empirical: a(n) = 15*a(n-1) -58*a(n-2) -13*a(n-3) +543*a(n-4) -1609*a(n-5) +1864*a(n-6) -17378*a(n-7) +62814*a(n-8) +73709*a(n-9) -307108*a(n-10) +721338*a(n-11) -862742*a(n-12) +4668915*a(n-13) -12478479*a(n-14) -3206649*a(n-15) +1858428*a(n-16) +5104796*a(n-17) +28929803*a(n-18) +21290844*a(n-19) +12857067*a(n-20) -28005842*a(n-21) -37205324*a(n-22) -26318800*a(n-23) -9161072*a(n-24) -1481856*a(n-25) -6336*a(n-26).

A224350 Number of nX5 0..2 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

Original entry on oeis.org

21, 441, 5840, 57387, 495985, 4231138, 37433596, 342170839, 3178789749, 29672959682, 277160393375, 2589242347971, 24204240827093, 226449704878547, 2120085885822119, 19857888410207651, 186050078426398273

Offset: 1

R. H. Hardin Apr 04 2013

nonn

Column 5 of A224353

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 56

Empirical recurrence of order 56 (see link above)

A224351 Number of nX6 0..2 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

Original entry on oeis.org

28, 784, 13052, 151010, 1421762, 12340932, 107694133, 977742699, 9202126546, 88363107023, 855357421083, 8298639299407, 80568348690372, 782845364074773, 7615402149223961, 74171368176011107, 723133239021563347

Offset: 1

R. H. Hardin Apr 04 2013

nonn

Column 6 of A224353

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 98

Empirical recurrence of order 98 (see link above)

A224352 Number of nX7 0..2 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

Original entry on oeis.org

36, 1296, 26610, 363392, 3816783, 34697869, 300892325, 2654062881, 24422915139, 233364588801, 2281743365906, 22551656451002, 223794737692968, 2224124508821224, 22127253845604143, 220432254659284132

Offset: 1

R. H. Hardin Apr 04 2013

nonn

Column 7 of A224353

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

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

A224354 Number of 3 X n 0..2 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

Original entry on oeis.org

27, 216, 788, 2321, 5840, 13052, 26610, 50423, 90012, 152912, 249120, 391589, 596768, 885188, 1282094, 1818123, 2530028, 3461448, 4663724, 6196761, 8129936, 10543052, 13527338, 17186495, 21637788, 27013184, 33460536, 41144813, 50249376

Offset: 1

R. H. Hardin, Apr 04 2013

nonn

Row 3 of A224353.

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

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

Cf. A224353.

Empirical: a(n) = (23/360)*n^6 + (19/40)*n^5 + (235/72)*n^4 + (61/8)*n^3 + (1921/180)*n^2 + (189/10)*n + 3 for n>1.
Conjectures from Colin Barker, Aug 29 2018: (Start)
G.f.: x*(27 + 27*x - 157*x^2 + 396*x^3 - 474*x^4 + 326*x^5 - 116*x^6 + 17*x^7) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>8.
(End)

A224355 Number of 4 X n 0..2 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

Original entry on oeis.org

81, 1296, 5880, 19608, 57387, 151010, 363392, 810436, 1693423, 3344982, 6292120, 11340202, 19682181, 33037788, 53827802, 85388930, 132235237, 200372476, 297672078, 434311972, 623291815, 881030622, 1228055196, 1689788168

Offset: 1

R. H. Hardin, Apr 04 2013

nonn

Row 4 of A224353.

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

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

Cf. A224353.

Empirical: a(n) = (41/4032)*n^8 + (9/112)*n^7 + (239/288)*n^6 + (109/24)*n^5 + (12079/576)*n^4 + (39/16)*n^3 + (310151/1008)*n^2 - (21299/84)*n + 142 for n>3.
Conjectures from Colin Barker, Aug 29 2018: (Start)
G.f.: x*(81 + 567*x - 2868*x^2 + 6540*x^3 - 6063*x^4 - 415*x^5 + 7550*x^6 - 8564*x^7 + 4918*x^8 - 1584*x^9 + 262*x^10 - 14*x^11) / (1 - x)^9.
a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>12.
(End)

A224356 Number of 5Xn 0..2 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

Original entry on oeis.org

243, 7776, 45064, 160362, 495985, 1421762, 3816783, 9630357, 22913143, 51614480, 110565824, 226229854, 443991585, 839005884, 1531899199, 2710956117, 4662807601, 7814081454, 12786980756, 20472326754, 32124242991, 49481371374

Offset: 1

R. H. Hardin Apr 04 2013

nonn

Row 5 of A224353

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

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

Empirical: a(n) = (1009/907200)*n^10 + (1489/181440)*n^9 + (7699/60480)*n^8 + (26497/30240)*n^7 + (234967/43200)*n^6 + (430969/8640)*n^5 - (23036177/181440)*n^4 + (81980567/45360)*n^3 - (18258277/8400)*n^2 + (3586529/630)*n - 10675 for n>5

A224357 Number of 6Xn 0..2 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

Original entry on oeis.org

729, 46656, 349280, 1351748, 4231138, 12340932, 34697869, 94262290, 246254814, 616242552, 1475123504, 3379586703, 7423803582, 15672970622, 31884279651, 62668814332, 119312143790, 220555944774, 396752366132, 695942226325

Offset: 1

R. H. Hardin Apr 04 2013

nonn

Row 6 of A224353

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

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

Empirical: a(n) = (761/8553600)*n^12 + (1733/3326400)*n^11 + (1459/108864)*n^10 + (4187/40320)*n^9 + (1551227/1814400)*n^8 + (72841/12600)*n^7 + (1802801/19440)*n^6 - (66259339/120960)*n^5 + (9020552353/1360800)*n^4 - (817656577/50400)*n^3 + (5508355001/83160)*n^2 - (57456263/1540)*n - 269256 for n>7

A224358 Number of 7Xn 0..2 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

Original entry on oeis.org

2187, 279936, 2710892, 11704964, 37433596, 107694133, 300892325, 834305212, 2288859662, 6150132424, 16041429234, 40392369273, 97941685953, 228592108824, 513973817853, 1114992467592, 2338135911280, 4749060805124, 9361861348424

Offset: 1

R. H. Hardin Apr 04 2013

nonn

Row 7 of A224353

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

R. H. Hardin, Table of n, a(n) for n = 1..116

Empirical: a(n) = (118519/21794572800)*n^14 + (2257/124540416)*n^13 + (126449/119750400)*n^12 + (175069/21772800)*n^11 + (49727/544320)*n^10 + (1018841/1451520)*n^9 + (447386489/76204800)*n^8 + (2968546327/21772800)*n^7 - (29364148727/21772800)*n^6 + (37983445967/2177280)*n^5 - (4238661826723/59875200)*n^4 + (1152210830677/3326400)*n^3 - (7620593288311/18918900)*n^2 + (1232004733/910)*n - 8483920 for n>9

cp's OEIS Frontend

A224348 Number of nX3 0..2 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

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A224349 Number of n X 4 0..2 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

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A224350 Number of nX5 0..2 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

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A224351 Number of nX6 0..2 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

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A224352 Number of nX7 0..2 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

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A224354 Number of 3 X n 0..2 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

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A224355 Number of 4 X n 0..2 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

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A224356 Number of 5Xn 0..2 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

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A224357 Number of 6Xn 0..2 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

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A224358 Number of 7Xn 0..2 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

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