A199647 -id:A199647 - cp's OEIS frontend

A199641 Number of n X 2 0..2 arrays with values 0..2 introduced in row major order and each element equal to one or two horizontal and vertical neighbors.

1, 3, 13, 60, 288, 1384, 6628, 31772, 152304, 730036, 3499340, 16773680, 80402532, 385399644, 1847365808, 8855120468, 42445929772, 203459338800, 975257291396, 4674775757500, 22407962058928, 107409807372276, 514855687878924

Offset: 1

R. H. Hardin, Nov 08 2011

nonn

Column 2 of A199647.

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

R. H. Hardin, Table of n, a(n) for n = 1..200

Cf. A199647.

Empirical: a(n) = 3*a(n-1) +7*a(n-2) +8*a(n-3) -8*a(n-5) for n>7.

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

A199642 Number of nX3 0..2 arrays with values 0..2 introduced in row major order and each element equal to one or two horizontal and vertical neighbors.

Original entry on oeis.org

1, 13, 112, 1265, 12748, 134748, 1396083, 14584050, 151837464, 1582988477, 16494233432, 171904221068, 1791430664487, 18669394073270, 194560012081184, 2027588187779377, 21130256645906468, 220206564513115724

Offset: 1

R. H. Hardin Nov 08 2011

nonn

Column 3 of A199647

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

R. H. Hardin, Table of n, a(n) for n = 1..200

Empirical: a(n) = 7*a(n-1) +41*a(n-2) -44*a(n-3) -111*a(n-4) -140*a(n-5) +291*a(n-6) -225*a(n-7) +511*a(n-8) +2150*a(n-9) -3007*a(n-10) -6248*a(n-11) -624*a(n-12) +19900*a(n-13) -14308*a(n-14) +15248*a(n-15) -13312*a(n-16) -1648*a(n-17) +21440*a(n-18) -5632*a(n-19) -3968*a(n-20) +5632*a(n-21) -14336*a(n-22) -8192*a(n-23) for n>24

A199643 Number of nX4 0..2 arrays with values 0..2 introduced in row major order and each element equal to one or two horizontal and vertical neighbors.

Original entry on oeis.org

2, 60, 1265, 29229, 658770, 15066222, 342328663, 7797114144, 177447181083, 4039488090307, 91947444344704, 2092999963213610, 47642308975551650, 1084472533833020100, 24685590900071146822, 561912613968766782369

Offset: 1

R. H. Hardin Nov 08 2011

nonn

Column 4 of A199647

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

R. H. Hardin, Table of n, a(n) for n = 1..200

A199644 Number of nX5 0..2 arrays with values 0..2 introduced in row major order and each element equal to one or two horizontal and vertical neighbors.

Original entry on oeis.org

3, 288, 12748, 658770, 32177372, 1614250077, 80053957248, 3988024796446, 198328767139736, 9869645990489747, 491026123739354858, 24431608808618462704, 1215575822472077464282, 60480991464785183388557

Offset: 1

R. H. Hardin Nov 08 2011

nonn

Column 5 of A199647

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

R. H. Hardin, Table of n, a(n) for n = 1..177

A199645 Number of nX6 0..2 arrays with values 0..2 introduced in row major order and each element equal to one or two horizontal and vertical neighbors.

Original entry on oeis.org

6, 1384, 134748, 15066222, 1614250077, 176701683386, 19161971644783, 2085499380111100, 226676302441401393, 24649864713781053665, 2680046304287719376722, 291407720701800854792287

Offset: 1

R. H. Hardin Nov 08 2011

nonn

Column 6 of A199647

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

R. H. Hardin, Table of n, a(n) for n = 1..30

A199640 Number of n X n 0..2 arrays with values 0..2 introduced in row major order and each element equal to one or two horizontal and vertical neighbors.

Original entry on oeis.org

0, 3, 112, 29229, 32177372, 176701683386, 4539946639286136

Offset: 1

R. H. Hardin Nov 08 2011

nonn

Diagonal of A199647

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

A199646 Number of nX7 0..2 arrays with values 0..2 introduced in row major order and each element equal to one or two horizontal and vertical neighbors.

Original entry on oeis.org

11, 6628, 1396083, 342328663, 80053957248, 19161971644783, 4539946639286136, 1079929763429897946, 256503858825070983388

Offset: 1

R. H. Hardin Nov 08 2011

nonn

Column 7 of A199647

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

cp's OEIS Frontend

A199641 Number of n X 2 0..2 arrays with values 0..2 introduced in row major order and each element equal to one or two horizontal and vertical neighbors.

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A199642 Number of nX3 0..2 arrays with values 0..2 introduced in row major order and each element equal to one or two horizontal and vertical neighbors.

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A199643 Number of nX4 0..2 arrays with values 0..2 introduced in row major order and each element equal to one or two horizontal and vertical neighbors.

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A199644 Number of nX5 0..2 arrays with values 0..2 introduced in row major order and each element equal to one or two horizontal and vertical neighbors.

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A199645 Number of nX6 0..2 arrays with values 0..2 introduced in row major order and each element equal to one or two horizontal and vertical neighbors.

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A199640 Number of n X n 0..2 arrays with values 0..2 introduced in row major order and each element equal to one or two horizontal and vertical neighbors.

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A199646 Number of nX7 0..2 arrays with values 0..2 introduced in row major order and each element equal to one or two horizontal and vertical neighbors.

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