A224409 -id:A224409 - cp's OEIS frontend

A224403 Number of n X n 0..1 arrays with rows unimodal and antidiagonals nondecreasing.

2, 12, 100, 884, 7812, 68282, 590254, 5055858, 42996954, 363652198, 3062704166, 25711681080, 215327121414, 1799987423914, 15026012170736, 125307656075926, 1044220994847456, 8697261784264396, 72413790737672880, 602789200212580366

Offset: 1

R. H. Hardin Apr 05 2013

nonn

Diagonal of A224409

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

R. H. Hardin, Table of n, a(n) for n = 1..50

A224404 Number of n X 3 0..1 arrays with rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

7, 28, 100, 358, 1288, 4636, 16684, 60040, 216064, 777544, 2798128, 10069552, 36237040, 130405312, 469286272, 1688808544, 6077472256, 21870844480, 78706050496, 283237457536, 1019279418112, 3668054858368, 13200135512320

Offset: 1

R. H. Hardin, Apr 05 2013

nonn

Column 3 of A224409.

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

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

Cf. A224409.

Empirical: a(n) = 4*a(n-1) - 2*a(n-2) + 2*a(n-3).

Empirical g.f.: x*(7 + 2*x^2) / (1 - 4*x + 2*x^2 - 2*x^3). - Colin Barker, Aug 30 2018

A224405 Number of n X 4 0..1 arrays with rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

11, 56, 228, 884, 3436, 13440, 52700, 206708, 810664, 3178940, 12465596, 48881440, 191679756, 751638532, 2947419144, 11557788332, 45321842028, 177721660896, 696904347580, 2732788270804, 10716150306024, 42021505514844

Offset: 1

R. H. Hardin, Apr 05 2013

nonn

Column 4 of A224409.

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

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

Cf. A224409.

Empirical: a(n) = 5*a(n-1) - 5*a(n-2) + 2*a(n-3) + 4*a(n-4).

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

A224406 Number of n X 5 0..1 arrays with rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

16, 101, 465, 1928, 7812, 31710, 129402, 529846, 2172346, 8908986, 36534670, 149811438, 614276002, 2518688490, 10327233902, 42344211246, 173621959826, 711894378346, 2918949452350, 11968441441998, 49073678703842

Offset: 1

R. H. Hardin, Apr 05 2013

nonn

Column 5 of A224409.

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

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

Cf. A224409.

Empirical: a(n) = 6*a(n-1) - 9*a(n-2) + 4*a(n-3) + 2*a(n-4) + 8*a(n-5).

Empirical g.f.: x*(1 - x)*(16 + 21*x + 24*x^2 + 7*x^3) / (1 - 6*x + 9*x^2 - 4*x^3 - 2*x^4 - 8*x^5). - Colin Barker, Aug 30 2018

A224407 Number of n X 6 0..1 arrays with rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

22, 169, 879, 3902, 16420, 68282, 284254, 1187830, 4979464, 20913026, 87905004, 369597368, 1554028138, 6533901986, 27470619810, 115492192540, 485546657850, 2041301158120, 8581884687952, 36079321433650, 151682073514422

Offset: 1

R. H. Hardin, Apr 05 2013

nonn

Column 6 of A224409.

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

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

Cf. A224409.

Empirical: a(n) = 7*a(n-1) -14*a(n-2) +9*a(n-3) +4*a(n-5) +16*a(n-6) for n>7.

Empirical g.f.: x*(22 + 15*x + 4*x^2 - 83*x^3 - 109*x^4 - 29*x^5 + 14*x^6) / (1 - 7*x + 14*x^2 - 9*x^3 - 4*x^5 - 16*x^6). - Colin Barker, Aug 30 2018

A224408 Number of n X 7 0..1 arrays with rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

29, 267, 1568, 7490, 32814, 139638, 590254, 2496332, 10583872, 44986080, 191565628, 816675452, 3483688120, 14864259432, 63428734440, 270666075032, 1154981259240, 4928419635424, 21029737949696, 89733758819456

Offset: 1

R. H. Hardin, Apr 05 2013

nonn

Column 7 of A224409.

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

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

Cf. A224409.

Empirical: a(n) = 8*a(n-1) - 20*a(n-2) + 18*a(n-3) - 4*a(n-4) + 2*a(n-5) + 8*a(n-6) + 32*a(n-7) for n>8.

Empirical g.f.: x*(29 + 35*x + 12*x^2 - 236*x^3 - 436*x^4 - 288*x^5 + 116*x^6 + 168*x^7) / (1 - 8*x + 20*x^2 - 18*x^3 + 4*x^4 - 2*x^5 - 8*x^6 - 32*x^7). - Colin Barker, Aug 30 2018

A224410 Number of 3 X n 0..1 arrays with rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

8, 36, 100, 228, 465, 879, 1568, 2668, 4362, 6890, 10560, 15760, 22971, 32781, 45900, 63176, 85612, 114384, 150860, 196620, 253477, 323499, 409032, 512724, 637550, 786838, 964296, 1174040, 1420623, 1709065, 2044884, 2434128, 2883408, 3399932

Offset: 1

R. H. Hardin, Apr 05 2013

nonn

Row 3 of A224409.

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

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

Cf. A224409.

Empirical: a(n) = (1/720)*n^6 + (1/48)*n^5 + (29/144)*n^4 + (13/16)*n^3 + (2087/360)*n^2 + (7/6)*n.
Conjectures from Colin Barker, Aug 30 2018: (Start)
G.f.: x*(8 - 20*x + 16*x^2 + 4*x^3 - 11*x^4 + 4*x^5) / (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>7.
(End)

A224411 Number of 4 X n 0..1 arrays with rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

16, 108, 358, 884, 1928, 3902, 7490, 13784, 24467, 42053, 70195, 114073, 180875, 280385, 425693, 634043, 927836, 1335806, 1894388, 2649298, 3657346, 4988504, 6728252, 8980226, 11869193, 15544379, 20183177, 25995263, 33227149, 42167203

Offset: 1

R. H. Hardin, Apr 05 2013

nonn

Row 4 of A224409.

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

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

Cf. A224409.

Empirical: a(n) = (1/40320)*n^8 + (1/1440)*n^7 + (31/2880)*n^6 + (13/144)*n^5 + (3767/5760)*n^4 + (6409/1440)*n^3 + (189859/10080)*n^2 - (73/24)*n - 7 for n>2.
Conjectures from Colin Barker, Aug 30 2018: (Start)
G.f.: x*(16 - 36*x - 38*x^2 + 206*x^3 - 196*x^4 - 106*x^5 + 368*x^6 - 334*x^7 + 155*x^8 - 38*x^9 + 4*x^10) / (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>11.
(End)

A224412 Number of 5Xn 0..1 arrays with rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

32, 324, 1288, 3436, 7812, 16420, 32814, 63202, 118117, 214919, 381436, 661132, 1120283, 1857749, 3018052, 4808608, 7522116, 11565280, 17495232, 26065236, 38281486, 55473066, 79377418, 112243966, 156958871, 217194245, 297585532

Offset: 1

R. H. Hardin Apr 05 2013

nonn

Row 5 of A224409

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

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

Empirical: a(n) = (1/3628800)*n^10 + (1/80640)*n^9 + (1/3456)*n^8 + (23/5760)*n^7 + (7213/172800)*n^6 + (683/2304)*n^5 + (138869/36288)*n^4 + (32143/2240)*n^3 + (32909/450)*n^2 - (753/20)*n - 44 for n>3

A224413 Number of 6Xn 0..1 arrays with rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

64, 972, 4636, 13440, 31710, 68282, 139638, 275766, 530583, 999049, 1844709, 3342831, 5946316, 10384152, 17805490, 29986574, 49622914, 80735424, 129226948, 203634878, 316136662, 483878162, 730710330, 1089437826, 1604704333

Offset: 1

R. H. Hardin Apr 05 2013

nonn

Row 6 of A224409

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

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

Empirical: a(n) = (1/479001600)*n^12 + (1/7257600)*n^11 + (199/43545600)*n^10 + (1/10752)*n^9 + (19951/14515200)*n^8 + (5143/345600)*n^7 + (6148357/43545600)*n^6 + (3015961/1451520)*n^5 + (128983289/10886400)*n^4 + (40193333/604800)*n^3 + (444089893/1663200)*n^2 - (4351/20)*n - 222 for n>4

cp's OEIS Frontend

A224403 Number of n X n 0..1 arrays with rows unimodal and antidiagonals nondecreasing.

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A224404 Number of n X 3 0..1 arrays with rows unimodal and antidiagonals nondecreasing.

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A224405 Number of n X 4 0..1 arrays with rows unimodal and antidiagonals nondecreasing.

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A224406 Number of n X 5 0..1 arrays with rows unimodal and antidiagonals nondecreasing.

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A224407 Number of n X 6 0..1 arrays with rows unimodal and antidiagonals nondecreasing.

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A224408 Number of n X 7 0..1 arrays with rows unimodal and antidiagonals nondecreasing.

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A224410 Number of 3 X n 0..1 arrays with rows unimodal and antidiagonals nondecreasing.

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A224411 Number of 4 X n 0..1 arrays with rows unimodal and antidiagonals nondecreasing.

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A224412 Number of 5Xn 0..1 arrays with rows unimodal and antidiagonals nondecreasing.

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A224413 Number of 6Xn 0..1 arrays with rows unimodal and antidiagonals nondecreasing.