A224146 -id:A224146 - cp's OEIS frontend

A224140 Number of n X n 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.

2, 9, 49, 272, 1509, 8375, 46586, 259927, 1454873, 8167578, 45975525, 259412481, 1466771294, 8308711329, 47142516717, 267868554552, 1524033271457, 8681096155047, 49500982033342, 282533898125471, 1614019099745197

Offset: 1

R. H. Hardin Mar 31 2013

nonn

Diagonal of A224146

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

R. H. Hardin, Table of n, a(n) for n = 1..22

A224141 Number of n X 3 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.

Original entry on oeis.org

7, 22, 49, 92, 155, 242, 357, 504, 687, 910, 1177, 1492, 1859, 2282, 2765, 3312, 3927, 4614, 5377, 6220, 7147, 8162, 9269, 10472, 11775, 13182, 14697, 16324, 18067, 19930, 21917, 24032, 26279, 28662, 31185, 33852, 36667, 39634, 42757, 46040, 49487, 53102

Offset: 1

R. H. Hardin, Mar 31 2013

nonn

Column 3 of A224146.

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

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

Cf. A224146.

Empirical: a(n) = (2/3)*n^3 + 2*n^2 + (13/3)*n.
Conjectures from Colin Barker, Aug 27 2018: (Start)
G.f.: x*(7 - 6*x + 3*x^2) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
(End)

A224142 Number of n X 4 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.

Original entry on oeis.org

11, 46, 124, 272, 526, 930, 1536, 2404, 3602, 5206, 7300, 9976, 13334, 17482, 22536, 28620, 35866, 44414, 54412, 66016, 79390, 94706, 112144, 131892, 154146, 179110, 206996, 238024, 272422, 310426, 352280, 398236, 448554, 503502, 563356, 628400

Offset: 1

R. H. Hardin, Mar 31 2013

nonn

Column 4 of A224146.

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

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

Cf. A224146.

Empirical: a(n) = (1/3)*n^4 + (4/3)*n^3 + (14/3)*n^2 + (23/3)*n - 4 for n>1.
Conjectures from Colin Barker, Aug 27 2018: (Start)
G.f.: x*(11 - 9*x + 4*x^2 + 2*x^3 + x^4 - x^5) / (1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>6.
(End)

A224143 Number of n X 5 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.

Original entry on oeis.org

16, 86, 275, 691, 1509, 2985, 5471, 9431, 15457, 24285, 36811, 54107, 77437, 108273, 148311, 199487, 263993, 344293, 443139, 563587, 709013, 883129, 1089999, 1334055, 1620113, 1953389, 2339515, 2784555, 3295021, 3877889, 4540615, 5291151, 6137961

Offset: 1

R. H. Hardin, Mar 31 2013

nonn

Column 5 of A224146.

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

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

Cf. A224146.

Empirical: a(n) = (2/15)*n^5 + (2/3)*n^4 + (10/3)*n^3 + (25/3)*n^2 + (203/15)*n - 17 for n>2.
Conjectures from Colin Barker, Aug 27 2018: (Start)
G.f.: x*(16 - 10*x - x^2 + 11*x^3 + 8*x^4 - 10*x^5 + x^6 + x^7) / (1 - x)^6.
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>8.
(End)

A224144 Number of n X 6 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.

Original entry on oeis.org

22, 148, 554, 1573, 3827, 8375, 16885, 31841, 56783, 96579, 157729, 248701, 380299, 566063, 822701, 1170553, 1634087, 2242427, 3029913, 4036693, 5309347, 6901543, 8874725, 11298833, 14253055, 17826611, 22119569, 27243693, 33323323, 40496287

Offset: 1

R. H. Hardin, Mar 31 2013

nonn

Column 6 of A224146.

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

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

Cf. A224146.

Empirical: a(n) = (2/45)*n^6 + (4/15)*n^5 + (16/9)*n^4 + 6*n^3 + (683/45)*n^2 + (341/15)*n - 55 for n>3.
Conjectures from Colin Barker, Aug 28 2018: (Start)
G.f.: x*(22 - 6*x - 20*x^2 + 33*x^3 + 40*x^4 - 53*x^5 + 8*x^6 + 11*x^7 - 2*x^8 - x^9) / (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>10.
(End)

A224145 Number of n X 7 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.

Original entry on oeis.org

29, 239, 1037, 3296, 8838, 21183, 46586, 95455, 184222, 337727, 592178, 998751, 1627894, 2574399, 3963306, 5956703, 8761486, 12638143, 17910626, 24977375, 34323558, 46534591, 62311002, 82484703, 108036734, 140116543, 180062866

Offset: 1

R. H. Hardin, Mar 31 2013

nonn

Column 7 of A224146.

			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..1..1..1..1..0....0..0..1..0..0..0..0....0..0..0..1..1..1..0
..0..0..1..1..1..1..1....0..0..1..0..0..0..0....0..0..0..1..1..1..1

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

Cf. A224146.

Empirical: a(n) = (4/315)*n^7 + (4/45)*n^6 + (34/45)*n^5 + (29/9)*n^4 + (508/45)*n^3 + (1156/45)*n^2 + (1328/35)*n - 161 for n>4.
Conjectures from Colin Barker, Aug 28 2018: (Start)
G.f.: x*(29 + 7*x - 63*x^2 + 68*x^3 + 152*x^4 - 199*x^5 + 28*x^6 + 71*x^7 - 21*x^8 - 12*x^9 + 3*x^10 + x^11) / (1 - x)^8.
a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>12.
(End)

A224147 Number of 3 X n 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.

Original entry on oeis.org

4, 16, 49, 124, 275, 554, 1037, 1831, 3082, 4984, 7789, 11818, 17473, 25250, 35753, 49709, 67984, 91600, 121753, 159832, 207439, 266410, 338837, 427091, 533846, 662104, 815221, 996934, 1211389, 1463170, 1757329, 2099417, 2495516, 2952272

Offset: 1

R. H. Hardin, Mar 31 2013

nonn

Row 3 of A224146.

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

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

Cf. A224146.

Empirical: a(n) = (1/720)*n^6 + (1/80)*n^5 + (23/144)*n^4 + (29/48)*n^3 + (241/180)*n^2 + (53/60)*n + 1.
Conjectures from Colin Barker, Aug 28 2018: (Start)
G.f.: x*(4 - 12*x + 21*x^2 - 23*x^3 + 16*x^4 - 6*x^5 + x^6) / (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)

A224148 Number of 4 X n 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.

Original entry on oeis.org

5, 25, 92, 272, 691, 1573, 3296, 6472, 12058, 21506, 36961, 61517, 99542, 157084, 242371, 366419, 543763, 793327, 1139450, 1613086, 2253197, 3108359, 4238602, 5717506, 7634576, 10097920, 13237255, 17207267, 22191352, 28405766, 36104213

Offset: 1

R. H. Hardin, Mar 31 2013

nonn

Row 4 of A224146.

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

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

Cf. A224146.

Empirical: a(n) = (1/40320)*n^8 + (1/3360)*n^7 + (1/192)*n^6 + (1/16)*n^5 + (223/640)*n^4 + (149/160)*n^3 + (3319/2016)*n^2 + (169/168)*n + 1.
Conjectures from Colin Barker, Aug 28 2018: (Start)
G.f.: x*(5 - 20*x + 47*x^2 - 76*x^3 + 85*x^4 - 62*x^5 + 29*x^6 - 8*x^7 + x^8) / (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>9.
(End)

A224149 Number of 5 X n 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.

Original entry on oeis.org

6, 36, 155, 526, 1509, 3827, 8838, 18969, 38392, 74053, 137204, 245636, 426869, 722624, 1194983, 1934737, 3072530, 4793530, 7356497, 11118274, 16564901, 24350745, 35347252, 50703161, 71918276, 100933171, 140237506, 192999960

Offset: 1

R. H. Hardin, Mar 31 2013

nonn

Row 5 of A224146.

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

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

Cf. A224146.

Empirical: a(n) = (1/3628800)*n^10 + (1/241920)*n^9 + (11/120960)*n^8 + (59/40320)*n^7 + (3853/172800)*n^6 + (181/1280)*n^5 + (100381/181440)*n^4 + (76319/60480)*n^3 + (24247/12600)*n^2 + (23/21)*n + 1.
Conjectures from Colin Barker, Aug 28 2018: (Start)
G.f.: x*(6 - 30*x + 89*x^2 - 189*x^3 + 288*x^4 - 309*x^5 + 236*x^6 - 127*x^7 + 46*x^8 - 10*x^9 + x^10) / (1 - x)^11.
a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11) for n>11.
(End)

A224150 Number of 6 X n 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.

Original entry on oeis.org

7, 49, 242, 930, 2985, 8375, 21183, 49365, 107697, 222603, 439909, 837071, 1542126, 2762572, 4828665, 8257309, 13844903, 22800305, 36932600, 58912756, 92633675, 143699769, 220085207, 333009601, 498091361, 736852507, 1078664659, 1563244537

Offset: 1

R. H. Hardin, Mar 31 2013

nonn

Row 6 of A224146.

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

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

Cf. A224146.

Empirical: a(n) = (1/479001600)*n^12 + (1/26611200)*n^11 + (43/43545600)*n^10 + (29/1451520)*n^9 + (5671/14515200)*n^8 + (2219/345600)*n^7 + (2174569/43545600)*n^6 + (116341/483840)*n^5 + (8531549/10886400)*n^4 + (2862857/1814400)*n^3 + (3602461/1663200)*n^2 + (2327/1980)*n + 1.
Conjectures from Colin Barker, Aug 28 2018: (Start)
G.f.: x*(7 - 42*x + 151*x^2 - 396*x^3 + 762*x^4 - 1076*x^5 + 1137*x^6 - 906*x^7 + 538*x^8 - 230*x^9 + 67*x^10 - 12*x^11 + x^12) / (1 - x)^13.
a(n) = 13*a(n-1) - 78*a(n-2) + 286*a(n-3) - 715*a(n-4) + 1287*a(n-5) - 1716*a(n-6) + 1716*a(n-7) - 1287*a(n-8) + 715*a(n-9) - 286*a(n-10) + 78*a(n-11) - 13*a(n-12) + a(n-13) for n>13.
(End)

cp's OEIS Frontend

A224140 Number of n X n 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.

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A224141 Number of n X 3 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.

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A224142 Number of n X 4 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.

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A224143 Number of n X 5 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.

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A224144 Number of n X 6 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.

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A224145 Number of n X 7 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.

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A224147 Number of 3 X n 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.

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A224148 Number of 4 X n 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.

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A224149 Number of 5 X n 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.

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