A229445 -id:A229445 - cp's OEIS frontend

A229439 Number of n X 2 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing.

4, 7, 13, 25, 47, 84, 142, 228, 350, 517, 739, 1027, 1393, 1850, 2412, 3094, 3912, 4883, 6025, 7357, 8899, 10672, 12698, 15000, 17602, 20529, 23807, 27463, 31525, 36022, 40984, 46442, 52428, 58975, 66117, 73889, 82327, 91468, 101350, 112012, 123494

Offset: 1

R. H. Hardin, Sep 23 2013

nonn

			Some solutions for n=4:
..0..2....0..2....0..2....1..1....0..2....0..2....0..2....0..0....0..2....0..2
..0..2....0..2....1..0....1..1....1..0....0..2....0..2....1..1....1..0....0..2
..0..2....0..2....2..1....1..1....1..0....1..0....1..0....2..2....2..1....1..0
..0..2....1..0....2..1....1..1....1..1....1..1....1..0....2..2....2..2....2..1

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

Column 2 of A229445.

Empirical: a(n) = (1/24)*n^4 + (1/12)*n^3 - (1/24)*n^2 + (23/12)*n + 2.
Conjectures from Colin Barker, Sep 16 2018: (Start)
G.f.: x*(4 - 13*x + 18*x^2 - 10*x^3 + 2*x^4) / (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>5.
(End)

A229440 Number of n X 3 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing.

Original entry on oeis.org

5, 10, 22, 53, 128, 293, 625, 1244, 2327, 4124, 6976, 11335, 17786, 27071, 40115, 58054, 82265, 114398, 156410, 210601, 279652, 366665, 475205, 609344, 773707, 973520, 1214660, 1503707, 1847998, 2255683, 2735783, 3298250, 3954029, 4715122

Offset: 1

R. H. Hardin, Sep 23 2013

nonn

			Some solutions for n=4:
..0..2..2....0..2..2....0..2..2....0..2..2....0..2..2....0..2..2....0..2..2
..1..0..2....0..2..2....1..0..2....0..2..2....0..2..2....1..0..0....1..0..2
..1..0..2....1..0..2....1..0..2....1..0..2....0..2..2....1..1..1....1..1..0
..1..0..2....2..1..0....1..1..0....1..1..0....1..0..2....2..2..2....1..1..0

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

Column 3 of A229445.

Empirical: a(n) = (1/360)*n^6 + (1/120)*n^5 + (1/36)*n^4 + (5/24)*n^3 - (11/360)*n^2 + (167/60)*n + 2.
Conjectures from Colin Barker, Sep 17 2018: (Start)
G.f.: x*(5 - 25*x + 57*x^2 - 66*x^3 + 44*x^4 - 15*x^5 + 2*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)

A229441 Number of n X 4 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing.

Original entry on oeis.org

6, 14, 37, 109, 324, 915, 2402, 5843, 13229, 28071, 56234, 107080, 194989, 341334, 576993, 945488, 1506848, 2342300, 3559899, 5301215, 7749202, 11137381, 15760476, 21986649, 30271487, 41173901, 55374104, 73693842, 97119059, 126825184

Offset: 1

R. H. Hardin, Sep 23 2013

nonn

			Some solutions for n=4:
..0..2..2..2....0..0..0..0....0..2..2..2....0..0..2..2....0..0..0..0
..1..0..0..0....1..1..1..1....1..0..2..2....0..0..2..2....1..1..1..1
..1..0..0..0....1..1..1..1....2..1..0..2....1..1..0..0....2..2..2..2
..1..1..1..1....2..2..2..2....2..2..1..0....2..2..1..1....2..2..2..2

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

Column 4 of A229445.

Empirical: a(n) = (1/5760)*n^8 + (1/2016)*n^7 + (1/576)*n^6 + (11/360)*n^5 + (409/5760)*n^4 + (49/288)*n^3 + (41/96)*n^2 + (2771/840)*n + 2.
Conjectures from Colin Barker, Sep 17 2018: (Start)
G.f.: x*(6 - 40*x + 127*x^2 - 224*x^3 + 255*x^4 - 177*x^5 + 77*x^6 - 19*x^7 + 2*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)

A229442 Number of n X 5 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing.

Original entry on oeis.org

7, 19, 60, 212, 753, 2546, 8024, 23428, 63430, 159945, 377840, 841419, 1777036, 3578998, 6908102, 12834739, 23041529, 40103959, 67871516, 111976374, 180501843, 284848554, 440842772, 670138334, 1001971536, 1475336877, 2141660944

Offset: 1

R. H. Hardin, Sep 23 2013

nonn

			Some solutions for n=4:
..0..0..0..0..2....0..2..2..2..2....0..0..2..2..2....0..2..2..2..2
..0..0..0..0..2....1..0..2..2..2....1..1..0..2..2....1..0..2..2..2
..1..1..1..1..0....1..1..0..2..2....1..1..1..0..0....1..1..0..0..0
..1..1..1..1..1....1..1..0..2..2....1..1..1..1..1....1..1..1..1..1

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

Column 5 of A229445.

Empirical: a(n) = (1/103680)*n^10 + (1/80640)*n^9 + (1/12096)*n^8 + (47/13440)*n^7 + (11/6912)*n^6 + (173/3840)*n^5 + (1187/10368)*n^4 + (12437/20160)*n^3 - (6211/10080)*n^2 + (4901/840)*n + 1.
Conjectures from Colin Barker, Sep 17 2018: (Start)
G.f.: x*(7 - 58*x + 236*x^2 - 558*x^3 + 896*x^4 - 941*x^5 + 709*x^6 - 343*x^7 + 103*x^8 - 17*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)

A229443 Number of nX6 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing.

Original entry on oeis.org

8, 25, 93, 387, 1609, 6374, 23610, 81177, 258698, 765702, 2113491, 5467941, 13331626, 30795942, 67738085, 142526854, 288060848, 561310955, 1057997269, 1934623043, 3440842683, 5966088386, 10105555904, 16752093179, 27222289586

Offset: 1

R. H. Hardin Sep 23 2013

nonn

Column 6 of A229445

			Some solutions for n=4
..0..0..0..2..2..2....0..0..2..2..2..2....0..0..0..2..2..2....0..0..2..2..2..2
..1..1..1..0..0..2....0..0..2..2..2..2....1..1..1..0..2..2....1..1..0..0..0..2
..1..1..1..1..1..0....1..1..0..2..2..2....1..1..1..1..0..2....2..2..1..1..1..0
..2..2..2..1..1..1....1..1..1..0..2..2....2..2..2..2..1..0....2..2..2..2..2..1

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

Empirical: a(n) = (73/159667200)*n^12 - (19/26611200)*n^11 + (19/2903040)*n^10 + (47/161280)*n^9 - (1259/1612800)*n^8 + (7711/806400)*n^7 - (10715/580608)*n^6 + (30575/96768)*n^5 - (4597853/3628800)*n^4 + (1198483/201600)*n^3 - (621689/55440)*n^2 + (168439/9240)*n - 4

A229444 Number of n X 7 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing.

Original entry on oeis.org

9, 32, 138, 665, 3184, 14536, 62205, 247607, 914271, 3133068, 9990129, 29755249, 83162347, 219151523, 547116607, 1299869098, 2951439969, 6429248828, 13483439736, 27310437901, 53577074678, 102061137870, 189220453845

Offset: 1

R. H. Hardin, Sep 23 2013

nonn

Column 7 of A229445.

			Some solutions for n=4
..0..0..0..0..2..2..2....0..0..0..2..2..2..2....0..0..2..2..2..2..2
..0..0..0..0..2..2..2....1..1..1..0..2..2..2....1..1..0..0..2..2..2
..1..1..1..1..0..0..0....1..1..1..1..0..2..2....1..1..1..1..0..0..0
..2..2..2..2..1..1..1....1..1..1..1..1..0..2....2..2..1..1..1..1..1

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

Cf. A229445.

Empirical: a(n) = (797/43589145600)*n^14 - (127/1245404160)*n^13 + (1/1451520)*n^12 + (335/19160064)*n^11 - (1381/10886400)*n^10 + (449/322560)*n^9 - (216523/30481920)*n^8 + (653459/8709120)*n^7 - (2384537/4838400)*n^6 + (2642473/870912)*n^5 - (275452937/23950080)*n^4 + (131909609/3991680)*n^3 - (38524939/687960)*n^2 + (21925483/360360)*n - 20.

A229446 Number of 3 X n 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing.

Original entry on oeis.org

8, 13, 22, 37, 60, 93, 138, 197, 272, 365, 478, 613, 772, 957, 1170, 1413, 1688, 1997, 2342, 2725, 3148, 3613, 4122, 4677, 5280, 5933, 6638, 7397, 8212, 9085, 10018, 11013, 12072, 13197, 14390, 15653, 16988, 18397, 19882, 21445, 23088, 24813, 26622, 28517

Offset: 1

R. H. Hardin, Sep 23 2013

nonn

			Some solutions for n=4:
..0..2..2..2....0..0..2..2....0..2..2..2....0..0..0..2....0..0..0..2
..1..0..2..2....0..0..2..2....1..0..2..2....1..1..1..0....0..0..0..2
..2..1..0..2....1..1..0..2....2..1..0..0....1..1..1..1....0..0..0..2

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

Row 3 of A229445.

Empirical: a(n) = (1/3)*n^3 + (8/3)*n + 5.
Conjectures from Colin Barker, Sep 17 2018: (Start)
G.f.: x*(8 - 19*x + 18*x^2 - 5*x^3) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
(End)

A229447 Number of 4 X n 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing.

Original entry on oeis.org

12, 25, 53, 109, 212, 387, 665, 1083, 1684, 2517, 3637, 5105, 6988, 9359, 12297, 15887, 20220, 25393, 31509, 38677, 47012, 56635, 67673, 80259, 94532, 110637, 128725, 148953, 171484, 196487, 224137, 254615, 288108, 324809, 364917, 408637, 456180

Offset: 1

R. H. Hardin, Sep 23 2013

nonn

			Some solutions for n=4:
..0..0..0..2....0..0..0..2....0..0..0..2....0..2..2..2....0..0..0..0
..1..1..1..0....1..1..1..0....1..1..1..0....1..0..2..2....1..1..1..1
..2..2..2..1....1..1..1..0....1..1..1..1....1..0..2..2....2..2..2..2
..2..2..2..2....2..2..2..1....2..2..2..1....2..1..0..2....2..2..2..2

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

Row 4 of A229445.

Empirical: a(n) = (1/4)*n^4 - (1/3)*n^3 + (13/4)*n^2 + (11/6)*n + 7.
Conjectures from Colin Barker, Sep 17 2018: (Start)
G.f.: x*(12 - 35*x + 48*x^2 - 26*x^3 + 7*x^4) / (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>5.
(End)

A229448 Number of 5 X n 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing.

Original entry on oeis.org

17, 47, 128, 324, 753, 1609, 3184, 5890, 10281, 17075, 27176, 41696, 61977, 89613, 126472, 174718, 236833, 315639, 414320, 536444, 685985, 867345, 1085376, 1345402, 1653241, 2015227, 2438232, 2929688, 3497609, 4150613, 4897944, 5749494, 6715825

Offset: 1

R. H. Hardin, Sep 23 2013

nonn

			Some solutions for n=4:
..0..0..2..2....0..2..2..2....0..0..0..2....0..0..2..2....0..0..2..2
..0..0..2..2....1..0..2..2....1..1..1..0....1..1..0..0....1..1..0..2
..1..1..0..0....2..1..0..2....1..1..1..0....1..1..0..0....1..1..1..0
..2..2..1..1....2..1..1..0....2..2..2..1....1..1..0..0....2..2..2..1
..2..2..2..2....2..2..1..1....2..2..2..2....1..1..0..0....2..2..2..2

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

Row 5 of A229445.

Empirical: a(n) = (11/60)*n^5 - (1/2)*n^4 + (15/4)*n^3 - 1*n^2 + (257/30)*n + 6.
Conjectures from Colin Barker, Sep 17 2018: (Start)
G.f.: x*(17 - 55*x + 101*x^2 - 79*x^3 + 44*x^4 - 6*x^5) / (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>6.
(End)

A229449 Number of 6 X n 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing.

Original entry on oeis.org

23, 84, 293, 915, 2546, 6374, 14536, 30571, 59969, 110816, 194535, 326723, 528084, 825458, 1252946, 1853131, 2678395, 3792332, 5271257, 7205811, 9702662, 12886302, 16900940, 21912491, 28110661, 35711128, 44957819, 56125283, 69521160, 85488746

Offset: 1

R. H. Hardin, Sep 23 2013

nonn

			Some solutions for n=4.
..0..0..0..0....0..2..2..2....0..2..2..2....0..2..2..2....0..2..2..2
..0..0..0..0....1..0..2..2....0..2..2..2....1..0..2..2....1..0..2..2
..0..0..0..0....2..1..0..0....0..2..2..2....1..1..0..2....1..1..0..2
..1..1..1..1....2..1..0..0....1..0..2..2....2..1..0..0....1..1..1..0
..2..2..2..2....2..2..1..1....1..0..2..2....2..1..0..0....2..1..1..0
..2..2..2..2....2..2..2..2....1..1..0..0....2..1..0..0....2..1..1..1

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

Row 6 of A229445.

Empirical: a(n) = (2/15)*n^6 - (5/8)*n^5 + (9/2)*n^4 - (55/8)*n^3 + (283/15)*n^2 - 4*n + 11.
Conjectures from Colin Barker, Sep 17 2018: (Start)
G.f.: x*(23 - 77*x + 188*x^2 - 177*x^3 + 159*x^4 - 31*x^5 + 11*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)

cp's OEIS Frontend

A229439 Number of n X 2 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing.

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A229440 Number of n X 3 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing.

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A229441 Number of n X 4 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing.

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A229442 Number of n X 5 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing.

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A229443 Number of nX6 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing.

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A229444 Number of n X 7 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing.

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A229446 Number of 3 X n 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing.

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A229447 Number of 4 X n 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing.

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A229448 Number of 5 X n 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing.

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A229449 Number of 6 X n 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing.

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