A211849 -id:A211849 - cp's OEIS frontend

A211842 Number of nonnegative integer arrays of length n+3 with new values 0 upwards introduced in order, no three adjacent elements all unequal, and containing the value 2.

1, 5, 19, 63, 196, 588, 1731, 5049, 14689, 42809, 125364, 369678, 1099339, 3300091, 10006487, 30658799, 94932890, 297079702, 939477265, 3001846219, 9689289277, 31586215805, 103968208826, 345457027212, 1158435912189, 3919502591649

Offset: 1

R. H. Hardin Apr 22 2012

nonn

Column 1 of A211849.

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

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

Cf. A211849.

A211843 Number of nonnegative integer arrays of length n+5 with new values 0 upwards introduced in order, no three adjacent elements all unequal, and containing the value 3.

Original entry on oeis.org

1, 7, 35, 147, 561, 2013, 6936, 23244, 76434, 248158, 799178, 2561866, 8197109, 26236283, 84147409, 270824081, 875656255, 2846900003, 9313478684, 30675454100, 101762486216, 340118043072, 1145518666868, 3888262008004, 13301838021901

Offset: 1

R. H. Hardin Apr 22 2012

nonn

Column 2 of A211849

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

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

A211844 Number of nonnegative integer arrays of length n+7 with new values 0 upwards introduced in order, no three adjacent elements all unequal, and containing the value 4.

Original entry on oeis.org

1, 9, 56, 286, 1302, 5486, 21897, 84003, 312864, 1139408, 4079404, 14417732, 50465519, 175400683, 606660198, 2091805472, 7201476498, 24786314450, 85384391951, 294672813537, 1019666296658, 3540327824374, 12341347668900

Offset: 1

R. H. Hardin Apr 22 2012

nonn

Column 3 of A211849

			Some solutions for n=3
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....1....1....0....0....1....1....1....1....0....1....1....1....1....0
..0....1....1....1....1....1....1....1....1....1....0....1....0....0....1....1
..0....2....2....2....1....1....2....2....2....2....1....2....0....0....2....1
..2....1....2....2....2....2....2....1....2....2....1....2....2....2....2....2
..2....1....3....3....2....2....0....1....3....2....2....3....2....0....2....2
..3....3....3....2....3....3....0....3....2....3....2....3....3....0....3....3
..3....3....4....2....3....3....3....3....2....2....3....4....3....3....3....3
..4....3....4....2....4....4....3....4....4....2....3....4....3....3....3....3
..4....4....0....4....4....3....4....3....2....4....4....4....4....4....4....4

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

A211845 Number of nonnegative integer arrays of length n+9 with new values 0 upwards introduced in order, no three adjacent elements all unequal, and containing the value 5.

Original entry on oeis.org

1, 11, 82, 494, 2619, 12713, 57913, 251481, 1052383, 4277451, 16986189, 66202629, 254144210, 963755936, 3618833405, 13481785125, 49915401836, 183932105682, 675399816338, 2474127510634, 9050295230250, 33087054691466, 120988345056414

Offset: 1

R. H. Hardin Apr 22 2012

nonn

Column 4 of A211849

			Some solutions for n=3
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....1....1....1....1....1....1....1....1....1....1....1....1....1....1
..1....1....1....1....0....1....1....1....1....1....1....1....1....1....1....1
..2....2....2....2....0....2....2....1....2....1....2....1....2....2....2....2
..2....2....1....1....2....2....2....2....1....2....2....2....2....2....2....1
..3....3....1....1....2....3....3....2....1....2....3....2....3....3....3....1
..3....3....3....3....3....3....3....3....3....3....2....2....3....2....3....3
..4....3....1....3....3....4....4....3....3....2....3....3....4....2....4....3
..4....4....1....4....4....4....4....4....4....2....3....3....4....4....4....4
..5....3....4....4....4....0....5....3....3....4....4....4....1....4....5....4
..5....3....4....5....5....0....5....3....3....4....4....4....1....4....4....5
..2....5....5....4....5....5....1....5....5....5....5....5....5....5....4....5

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

A211846 Number of nonnegative integer arrays of length n+11 with new values 0 upwards introduced in order, no three adjacent elements all unequal, and containing the value 6.

Original entry on oeis.org

1, 13, 113, 785, 4755, 26163, 134164, 651814, 3035018, 13657458, 59769854, 255628486, 1072565093, 4428689165, 18041493575, 72667375995, 289905733805, 1147339718965, 4510476836460, 17634066423470, 68632042506612

Offset: 1

R. H. Hardin Apr 22 2012

nonn

Column 5 of A211849

			Some solutions for n=3
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....1....1....1....1....1....1....1....1....1....1....0....1....1....0
..1....1....1....1....1....1....1....1....1....1....1....1....1....0....1....1
..2....2....2....2....2....2....2....2....2....2....2....2....1....0....2....1
..2....1....2....2....2....2....2....2....2....2....2....2....2....2....2....2
..3....1....3....3....3....3....3....2....1....3....3....3....2....2....3....2
..3....3....3....3....3....3....2....3....1....3....3....3....2....3....3....3
..4....3....4....4....4....4....2....3....3....4....2....3....3....3....3....2
..4....4....3....4....4....4....4....3....3....4....2....4....3....4....4....2
..5....4....3....5....5....3....4....4....4....4....4....4....4....4....4....4
..5....4....5....5....4....3....4....4....4....5....4....5....4....5....5....4
..6....5....5....6....4....5....5....5....5....5....5....4....5....5....5....5
..6....5....5....5....4....5....5....5....5....6....5....4....5....6....6....5
..3....6....6....6....6....6....6....6....6....6....6....6....6....5....5....6

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

A211847 Number of nonnegative integer arrays of length n+13 with new values 0 upwards introduced in order, no three adjacent elements all unequal, and containing the value 7.

Original entry on oeis.org

1, 15, 149, 1173, 7996, 49210, 280751, 1510267, 7752966, 38313584, 183476493, 855810005, 3904023943, 17474944971, 76959615336, 334220597220, 1434013918092, 6088757186340, 25619291046722, 106954200571650, 443491592171780

Offset: 1

R. H. Hardin Apr 22 2012

nonn

Column 6 of A211849.

			Some solutions for n=3
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....1....1....1....1....1....1....1....0....1....0....1....1....1....1
..1....1....1....1....1....1....1....0....1....1....0....1....1....1....0....1
..2....1....2....2....2....2....2....0....2....1....0....1....2....2....0....2
..2....2....2....2....2....2....2....2....2....1....2....2....2....2....2....2
..3....2....3....3....3....3....3....2....3....2....2....2....3....3....2....3
..2....3....3....3....3....3....3....3....3....2....2....3....3....2....3....3
..3....3....4....4....3....3....4....3....4....3....3....3....4....2....3....4
..3....4....4....4....4....3....4....4....4....3....3....4....4....4....4....3
..4....4....5....4....4....4....1....4....4....4....4....4....5....4....4....4
..4....5....5....5....5....4....1....4....5....4....4....4....4....5....5....4
..5....5....3....5....5....5....5....5....5....5....5....5....4....5....5....5
..5....5....3....5....6....5....5....5....6....5....5....5....6....6....6....5
..6....6....6....6....6....6....6....6....6....6....6....6....6....5....6....6
..6....6....6....6....6....6....6....6....6....6....6....6....7....5....7....6
..7....7....7....7....7....7....7....7....7....7....7....7....6....7....6....7

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

Cf. A211849.

A211848 Number of nonnegative integer arrays of length n+15 with new values 0 upwards introduced in order, no three adjacent elements all unequal, and containing the value 8.

Original entry on oeis.org

1, 17, 190, 1672, 12671, 86275, 542235, 3200979, 17970009, 96806505, 503889439, 2547775803, 12567000344, 60679921204, 287630757639, 1341627687593, 6170270168142, 28028072584878, 125932459466866, 560392344329658

Offset: 1

R. H. Hardin Apr 22 2012

nonn

Column 7 of A211849

			Some solutions for n=3
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....1....1....1....1....1....1....1....1....1....0....1....1....1....1
..1....1....1....1....0....1....1....1....1....1....1....1....1....1....1....1
..2....2....1....1....0....2....2....2....2....2....2....1....1....2....1....2
..2....2....2....2....2....1....2....2....2....1....2....2....2....1....2....2
..3....3....2....2....2....1....3....3....3....1....3....2....2....1....1....3
..3....3....3....3....3....3....3....3....3....3....3....3....3....3....1....2
..4....3....3....3....3....3....4....4....3....3....4....3....3....3....3....2
..4....4....4....4....4....4....3....4....4....4....4....4....4....4....3....4
..5....4....4....4....3....4....3....5....4....4....5....4....4....4....4....4
..5....5....5....5....3....5....5....5....5....4....5....5....5....5....4....5
..0....5....5....5....5....4....5....6....4....5....6....5....5....5....5....5
..0....6....6....6....5....4....6....6....4....5....5....6....6....6....5....6
..6....6....6....6....6....6....6....7....6....6....5....6....6....6....6....5
..6....7....7....6....6....6....7....7....6....6....5....7....7....7....6....5
..7....7....7....7....7....7....6....8....7....7....7....7....7....7....7....7
..7....8....8....7....7....7....6....7....7....7....7....8....8....8....7....7
..8....8....8....8....8....8....8....7....8....8....8....7....7....8....8....8

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

A211850 Number of nonnegative integer arrays of length 2n+5 with new values 0 upwards introduced in order, no three adjacent elements all unequal, and containing the value n+1.

Original entry on oeis.org

63, 147, 286, 494, 785, 1173, 1672, 2296, 3059, 3975, 5058, 6322, 7781, 9449, 11340, 13468, 15847, 18491, 21414, 24630, 28153, 31997, 36176, 40704, 45595, 50863, 56522, 62586, 69069, 75985, 83348, 91172, 99471, 108259, 117550, 127358, 137697, 148581

Offset: 1

R. H. Hardin, Apr 22 2012

nonn

Row 4 of A211849.

			Some solutions for n=3:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....0....1....1....0....0....1....1....1....1....1....1....1....1....1
..1....1....0....1....1....1....1....1....1....1....1....1....1....1....0....0
..1....1....1....2....2....1....1....2....1....2....0....2....2....2....0....0
..2....2....1....2....2....0....2....2....2....2....0....2....2....2....0....0
..2....2....2....3....2....0....2....2....2....3....2....3....3....3....2....2
..2....3....2....3....3....2....3....3....3....2....0....3....3....3....2....2
..3....2....2....4....2....2....2....2....3....2....0....3....1....3....3....3
..2....2....3....4....2....3....2....2....4....4....3....0....1....4....3....3
..2....4....3....3....4....3....2....4....4....4....3....0....1....4....3....4
..4....4....4....3....2....4....4....4....2....0....4....4....4....5....4....4

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

Cf. A211849.

Empirical: a(n) = (7/3)*n^3 + (27/2)*n^2 + (163/6)*n + 20.
Conjectures from Colin Barker, Jul 20 2018: (Start)
G.f.: x*(63 - 105*x + 76*x^2 - 20*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)

A211851 Number of nonnegative integer arrays of length 2n+6 with new values 0 upwards introduced in order, no three adjacent elements all unequal, and containing the value n+1.

Original entry on oeis.org

196, 561, 1302, 2619, 4755, 7996, 12671, 19152, 27854, 39235, 53796, 72081, 94677, 122214, 155365, 194846, 241416, 295877, 359074, 431895, 515271, 610176, 717627, 838684, 974450, 1126071, 1294736, 1481677, 1688169, 1915530, 2165121, 2438346

Offset: 1

R. H. Hardin, Apr 22 2012

nonn

Row 5 of A211849.

			Some solutions for n=3:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....1....1....1....0....1....0....1....1....1....1....1....1....0....1....1
..1....1....1....1....1....0....1....0....1....1....1....1....1....0....1....1
..1....1....2....1....1....0....1....0....2....2....2....2....2....1....2....1
..2....2....2....2....2....2....1....2....2....2....1....2....1....1....2....2
..2....1....2....1....1....2....2....2....2....3....1....2....1....2....3....1
..3....1....3....1....1....3....2....2....3....2....1....3....3....2....2....1
..3....3....3....1....1....3....0....3....3....2....1....3....3....3....2....3
..0....3....3....3....3....3....0....3....3....4....3....4....4....3....3....3
..0....4....4....3....3....3....3....2....4....2....3....3....3....4....2....4
..4....4....3....4....4....4....3....2....4....4....3....3....4....3....2....4
..0....5....3....3....3....4....4....4....3....2....4....0....4....4....4....2

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

Cf. A211849.

Empirical: a(n) = (43/24)*n^4 + (185/12)*n^3 + (1217/24)*n^2 + (937/12)*n + 50.
Conjectures from Colin Barker, Jul 20 2018: (Start)
G.f.: x*(196 - 419*x + 457*x^2 - 241*x^3 + 50*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)

A211852 Number of nonnegative integer arrays of length 2n+7 with new values 0 upwards introduced in order, no three adjacent elements all unequal, and containing the value n+1.

Original entry on oeis.org

588, 2013, 5486, 12713, 26163, 49210, 86275, 142968, 226230, 344475, 507732, 727787, 1018325, 1395072, 1875937, 2481154, 3233424, 4158057, 5283114, 6639549, 8261351, 10185686, 12453039, 15107356, 18196186, 21770823, 25886448, 30602271

Offset: 1

R. H. Hardin, Apr 22 2012

nonn

Row 6 of A211849.

			Some solutions for n=3:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....1....0....1....1....1....1....1....1....0....1....1....1....1....1
..0....1....1....1....1....1....1....1....1....1....1....1....1....1....1....0
..0....2....2....1....2....0....2....2....2....2....1....2....1....1....2....0
..2....1....1....2....2....0....2....2....2....1....1....2....2....2....2....2
..2....1....1....2....2....2....1....2....3....1....0....3....2....2....2....2
..2....3....0....2....2....2....1....2....2....3....0....3....3....1....2....3
..3....3....0....3....3....3....3....3....3....1....2....3....3....1....2....3
..3....4....3....3....3....2....3....3....3....1....2....3....4....3....3....4
..4....4....3....4....4....2....3....2....4....2....3....3....3....1....3....4
..3....3....3....4....3....2....4....2....4....2....3....3....3....1....2....3
..3....4....4....4....3....4....4....2....5....4....4....4....1....4....2....3
..2....3....4....4....0....4....3....4....5....4....4....3....3....4....4....3

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

Cf. A211849.

Empirical: a(n) = (71/60)*n^5 + (337/24)*n^4 + 67*n^3 + (3947/24)*n^2 + (12919/60)*n + 126.
Conjectures from Colin Barker, Jul 20 2018: (Start)
G.f.: x*(588 - 1515*x + 2228*x^2 - 1768*x^3 + 735*x^4 - 126*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)

cp's OEIS Frontend

A211842 Number of nonnegative integer arrays of length n+3 with new values 0 upwards introduced in order, no three adjacent elements all unequal, and containing the value 2.

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A211843 Number of nonnegative integer arrays of length n+5 with new values 0 upwards introduced in order, no three adjacent elements all unequal, and containing the value 3.

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A211844 Number of nonnegative integer arrays of length n+7 with new values 0 upwards introduced in order, no three adjacent elements all unequal, and containing the value 4.

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A211845 Number of nonnegative integer arrays of length n+9 with new values 0 upwards introduced in order, no three adjacent elements all unequal, and containing the value 5.

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A211846 Number of nonnegative integer arrays of length n+11 with new values 0 upwards introduced in order, no three adjacent elements all unequal, and containing the value 6.

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A211847 Number of nonnegative integer arrays of length n+13 with new values 0 upwards introduced in order, no three adjacent elements all unequal, and containing the value 7.

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A211848 Number of nonnegative integer arrays of length n+15 with new values 0 upwards introduced in order, no three adjacent elements all unequal, and containing the value 8.

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A211850 Number of nonnegative integer arrays of length 2n+5 with new values 0 upwards introduced in order, no three adjacent elements all unequal, and containing the value n+1.

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A211851 Number of nonnegative integer arrays of length 2n+6 with new values 0 upwards introduced in order, no three adjacent elements all unequal, and containing the value n+1.

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A211852 Number of nonnegative integer arrays of length 2n+7 with new values 0 upwards introduced in order, no three adjacent elements all unequal, and containing the value n+1.

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