A239155 -id:A239155 - cp's OEIS frontend

A239150 Number of (n+1) X (1+1) 0..3 arrays with no element equal to all horizontal neighbors or unequal to all vertical neighbors, and new values 0..3 introduced in row major order.

1, 1, 7, 17, 96, 340, 1639, 6623, 29843, 126163, 554310, 2380524, 10363965, 44756085, 194216303, 840357677, 3642433780, 15771490916, 68331367227, 295943443667, 1282011757819, 5552887116543, 24053558944522, 104188496250108

Offset: 1

R. H. Hardin, Mar 11 2014

nonn

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

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

Column 1 of A239155.

Empirical: a(n) = 4*a(n-1) + 7*a(n-2) - 26*a(n-3) + 5*a(n-4) + 14*a(n-5).

Empirical g.f.: x*(1 - 3*x - 4*x^2 + 8*x^3) / ((1 - x - x^2)*(1 - 3*x - 9*x^2 + 14*x^3)).

A239151 Number of (n+1)X(2+1) 0..3 arrays with no element equal to all horizontal neighbors or unequal to all vertical neighbors, and new values 0..3 introduced in row major order.

Original entry on oeis.org

2, 2, 55, 208, 2778, 17050, 166531, 1221727, 10652903, 83558723, 698912193, 5620874008, 46297856418, 375826633534, 3078013187839, 25072750273992, 204911552403250, 1671311190316246, 13648365689804011, 111372868203567131

Offset: 1

R. H. Hardin, Mar 11 2014

nonn

Column 2 of A239155

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

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

Empirical: a(n) = 4*a(n-1) +51*a(n-2) -84*a(n-3) -529*a(n-4) +442*a(n-5) +1605*a(n-6) +1916*a(n-7) -5423*a(n-8) -5800*a(n-9) +8753*a(n-10) +890*a(n-11) -5088*a(n-12) +4464*a(n-13) +3456*a(n-14)

A239152 Number of (n+1)X(3+1) 0..3 arrays with no element equal to all horizontal neighbors or unequal to all vertical neighbors, and new values 0..3 introduced in row major order.

Original entry on oeis.org

7, 7, 868, 5775, 209839, 2709568, 63961519, 1049404191, 21350167780, 381843947671, 7373045875687, 135997241404032, 2577824537597143, 48074166516591223, 905276493099636196, 16948804700642238303

Offset: 1

R. H. Hardin, Mar 11 2014

nonn

Column 3 of A239155

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

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

Empirical: a(n) = 20*a(n-1) +86*a(n-2) -2504*a(n-3) +7634*a(n-4) +21878*a(n-5) -95663*a(n-6) +32018*a(n-7) +100940*a(n-8) -38416*a(n-9)

A239153 Number of (n+1)X(4+1) 0..3 arrays with no element equal to all horizontal neighbors or unequal to all vertical neighbors, and new values 0..3 introduced in row major order.

Original entry on oeis.org

24, 24, 12159, 135766, 12844591, 330311070, 18120156500, 629468400383, 28646802159654, 1108832844851022, 47257467282260746, 1901383445656471050, 79172996011297669608, 3229805113653824580575, 133380680053667604594194

Offset: 1

R. H. Hardin, Mar 11 2014

nonn

Column 4 of A239155

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

R. H. Hardin, Table of n, a(n) for n = 1..55

A239156 Number of (3+1)X(n+1) 0..3 arrays with no element equal to all horizontal neighbors or unequal to all vertical neighbors, and new values 0..3 introduced in row major order.

Original entry on oeis.org

7, 55, 868, 12159, 175471, 2519488, 36221263, 520615791, 7483320292, 107564015719, 1546111034695, 22223587182336, 319438814614615, 4591569914960743, 65998599449004004, 948654862324898319

Offset: 1

R. H. Hardin, Mar 11 2014

nonn

Row 3 of A239155

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

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

Empirical: a(n) = 14*a(n-1) +14*a(n-2) -124*a(n-3) -6*a(n-4) +90*a(n-5) -27*a(n-6)

A239157 Number of (4+1)X(n+1) 0..3 arrays with no element equal to all horizontal neighbors or unequal to all vertical neighbors, and new values 0..3 introduced in row major order.

Original entry on oeis.org

17, 208, 5775, 135766, 3313304, 80240064, 1946535209, 47203774762, 1144788832875, 27763021735024, 673301630092412, 16328724383102508, 395999761775761841, 9603677662310968264, 232905759724044440751

Offset: 1

R. H. Hardin, Mar 11 2014

nonn

Row 4 of A239155

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

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

Empirical: a(n) = 20*a(n-1) +125*a(n-2) -466*a(n-3) -1721*a(n-4) +3476*a(n-5) +3342*a(n-6) -3082*a(n-7) -5349*a(n-8) -4488*a(n-9) +8976*a(n-10) +2826*a(n-11) -2862*a(n-12) -324*a(n-13) +243*a(n-14)

A239158 Number of (5+1)X(n+1) 0..3 arrays with no element equal to all horizontal neighbors or unequal to all vertical neighbors, and new values 0..3 introduced in row major order.

Original entry on oeis.org

96, 2778, 209839, 12844591, 821135900, 52019283568, 3301711870920, 209479341898544, 13291665794245067, 843354268309287289, 53510901660533324714, 3395268764228553206688, 215429967962178289895220

Offset: 1

R. H. Hardin, Mar 11 2014

nonn

Row 5 of A239155

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 57

Empirical recurrence of order 57 (see link above)

A239159 Number of (6+1)X(n+1) 0..3 arrays with no element equal to all horizontal neighbors or unequal to all vertical neighbors, and new values 0..3 introduced in row major order.

Original entry on oeis.org

340, 17050, 2709568, 330311070, 42600989632, 5427557363908, 693325664438772, 88515970694682238, 11302116207196944184, 1443066224926757673588, 184253299972460754777622, 23525764336051214515515358

Offset: 1

R. H. Hardin, Mar 11 2014

nonn

Row 6 of A239155

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

R. H. Hardin, Table of n, a(n) for n = 1..154

A239160 Number of (7+1)X(n+1) 0..3 arrays with no element equal to all horizontal neighbors or unequal to all vertical neighbors, and new values 0..3 introduced in row major order.

Original entry on oeis.org

1639, 166531, 63961519, 18120156500, 5469574400477, 1628795409782566, 486439997897622259, 145186363056322713567, 43339017958528994310740, 12936602480737955657135546, 3861570524893536530703944116

Offset: 1

R. H. Hardin, Mar 11 2014

nonn

Row 7 of A239155

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

R. H. Hardin, Table of n, a(n) for n = 1..42

A239149 Number of (n+1)X(n+1) 0..3 arrays with no element equal to all horizontal neighbors or unequal to all vertical neighbors, and new values 0..3 introduced in row major order.

Original entry on oeis.org

1, 2, 868, 135766, 821135900, 5427557363908, 486439997897622259, 105891766683961733641397

Offset: 1

R. H. Hardin, Mar 11 2014

nonn

Diagonal of A239155

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

cp's OEIS Frontend

A239150 Number of (n+1) X (1+1) 0..3 arrays with no element equal to all horizontal neighbors or unequal to all vertical neighbors, and new values 0..3 introduced in row major order.

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A239151 Number of (n+1)X(2+1) 0..3 arrays with no element equal to all horizontal neighbors or unequal to all vertical neighbors, and new values 0..3 introduced in row major order.

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A239152 Number of (n+1)X(3+1) 0..3 arrays with no element equal to all horizontal neighbors or unequal to all vertical neighbors, and new values 0..3 introduced in row major order.

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A239153 Number of (n+1)X(4+1) 0..3 arrays with no element equal to all horizontal neighbors or unequal to all vertical neighbors, and new values 0..3 introduced in row major order.

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A239156 Number of (3+1)X(n+1) 0..3 arrays with no element equal to all horizontal neighbors or unequal to all vertical neighbors, and new values 0..3 introduced in row major order.

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A239157 Number of (4+1)X(n+1) 0..3 arrays with no element equal to all horizontal neighbors or unequal to all vertical neighbors, and new values 0..3 introduced in row major order.

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A239158 Number of (5+1)X(n+1) 0..3 arrays with no element equal to all horizontal neighbors or unequal to all vertical neighbors, and new values 0..3 introduced in row major order.

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A239159 Number of (6+1)X(n+1) 0..3 arrays with no element equal to all horizontal neighbors or unequal to all vertical neighbors, and new values 0..3 introduced in row major order.

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A239160 Number of (7+1)X(n+1) 0..3 arrays with no element equal to all horizontal neighbors or unequal to all vertical neighbors, and new values 0..3 introduced in row major order.

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A239149 Number of (n+1)X(n+1) 0..3 arrays with no element equal to all horizontal neighbors or unequal to all vertical neighbors, and new values 0..3 introduced in row major order.

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