A197250 -id:A197250 - cp's OEIS frontend

A197244 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,0,1,1,1 for x=0,1,2,3,4.

2, 4, 8, 16, 40, 80, 192, 400, 936, 1984, 4576, 9824, 22408, 48560, 109888, 239728, 539432, 1182432, 2649952, 5828544, 13024648, 28717648, 64040768, 141448528, 314965928, 696544000, 1549366240, 3429474848, 7622621832, 16883244016

Offset: 1

R. H. Hardin, Oct 12 2011

nonn

Every 0 is next to 0 0's, every 1 is next to 1 0's, every 2 is next to 2 1's, every 3 is next to 3 1's, every 4 is next to 4 1's.

Column 2 of A197250.

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

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

Cf. A197250.

Empirical: a(n) = 4*a(n-2) +2*a(n-3) +a(n-4) -2*a(n-5).

Empirical g.f.: 2*x*(1 - x)*(1 + x)^3 / (1 - 4*x^2 - 2*x^3 - x^4 + 2*x^5). - Colin Barker, May 11 2018

A197245 Number of nX3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,0,1,1,1 for x=0,1,2,3,4.

Original entry on oeis.org

1, 8, 3, 53, 110, 227, 1035, 2004, 7529, 20633, 53902, 172997, 474139, 1395792, 4009631, 11336881, 33563326, 95906965, 275694011, 796470870, 2294495057, 6647188965, 19110664400, 55033208033, 159018294491, 458707454692

Offset: 1

R. H. Hardin Oct 12 2011

nonn

Every 0 is next to 0 0's, every 1 is next to 1 0's, every 2 is next to 2 1's, every 3 is next to 3 1's, every 4 is next to 4 1's

Column 3 of A197250

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

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

Empirical: a(n) = a(n-2) +9*a(n-3) +26*a(n-4) +58*a(n-5) -25*a(n-6) -148*a(n-7) -104*a(n-8) -114*a(n-9) +55*a(n-10) -149*a(n-11) +186*a(n-12) -9*a(n-13) +39*a(n-14) -55*a(n-15) +21*a(n-16) +a(n-17) +2*a(n-18) -a(n-19) for n>20

A197246 Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,0,1,1,1 for x=0,1,2,3,4.

Original entry on oeis.org

1, 16, 53, 275, 780, 5713, 16773, 98870, 393913, 1869033, 8527840, 32730687, 177791439, 674100600, 3386483171, 13856198755, 66236228308, 289604893615, 1242844626331, 5912414575588, 24990706118619, 116867053171491

Offset: 1

R. H. Hardin Oct 12 2011

nonn

Every 0 is next to 0 0's, every 1 is next to 1 0's, every 2 is next to 2 1's, every 3 is next to 3 1's, every 4 is next to 4 1's

Column 4 of A197250

			Some solutions containing all values 0 to 4 for n=5
..0..1..1..0....1..1..0..1....0..1..1..0....1..0..1..2....0..1..1..0
..1..2..3..1....0..1..3..1....2..1..4..1....3..1..4..1....1..3..2..1
..1..0..1..3....1..4..1..0....1..0..1..2....1..4..1..0....3..1..0..1
..1..1..4..1....3..1..4..1....2..1..1..0....0..1..3..1....1..4..1..1
..0..1..1..0....1..0..1..2....0..1..3..1....1..1..0..1....0..1..2..0

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

Empirical: a(n) = 5*a(n-2) +12*a(n-3) +134*a(n-4) +160*a(n-5) -615*a(n-6) +12174*a(n-7) -518*a(n-8) -47245*a(n-9) -44364*a(n-10) +38534*a(n-11) +120522*a(n-12) -170702*a(n-13) -87919*a(n-14) -4472*a(n-15) +682511*a(n-16) -390368*a(n-17) +333704*a(n-18) -949248*a(n-19) +1346705*a(n-20) -1109007*a(n-21) +1033190*a(n-22) -2853866*a(n-23) +1697513*a(n-24) +872394*a(n-25) +1858574*a(n-26) +533223*a(n-27) -3166721*a(n-28) +1038785*a(n-29) -2246717*a(n-30) +2216266*a(n-31) -1520506*a(n-32) +1327738*a(n-33) -734503*a(n-34) +531200*a(n-35) -302942*a(n-36) +85056*a(n-37) -52786*a(n-38) +18048*a(n-39) +9507*a(n-40) -770*a(n-41) +911*a(n-42) -852*a(n-43) +25*a(n-44) +25*a(n-45) -180*a(n-46) -55*a(n-47) +15*a(n-48) +10*a(n-49) for n>50

A197247 Number of nX5 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,0,1,1,1 for x=0,1,2,3,4.

Original entry on oeis.org

3, 40, 110, 780, 5062, 31276, 213912, 1244680, 8149652, 54813300, 363207297, 2334210952, 15099425049, 99496688244, 657733281792, 4291822021778, 27959094118746, 183056501656614, 1201021999376817, 7872982494463940

Offset: 1

R. H. Hardin Oct 12 2011

nonn

Every 0 is next to 0 0's, every 1 is next to 1 0's, every 2 is next to 2 1's, every 3 is next to 3 1's, every 4 is next to 4 1's

Column 5 of A197250

			Some solutions containing all values 0 to 4 for n=4
..0..1..3..1..0....1..0..2..1..0....1..0..2..1..0....0..1..1..2..0
..1..4..1..4..1....3..1..1..4..1....3..1..1..4..1....1..3..0..1..1
..2..1..0..1..2....1..3..0..1..2....1..1..0..1..1....3..1..1..4..1
..0..2..1..1..0....0..1..1..2..0....0..2..1..2..0....1..0..1..1..0

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

A197248 Number of nX6 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,0,1,1,1 for x=0,1,2,3,4.

Original entry on oeis.org

3, 80, 227, 5713, 31276, 405065, 3264225, 29975706, 324191969, 2687575073, 30493965518, 259733680667, 2634174755809, 25422825883256, 236887111563899, 2418154978600875, 22091513472216108, 220206294709791833

Offset: 1

R. H. Hardin Oct 12 2011

nonn

Every 0 is next to 0 0's, every 1 is next to 1 0's, every 2 is next to 2 1's, every 3 is next to 3 1's, every 4 is next to 4 1's

Column 6 of A197250

			Some solutions containing all values 0 to 4 for n=4
..1..2..0..1..2..0....1..1..0..1..1..0....0..2..1..0..1..1....2..1..0..1..1..2
..0..1..1..4..1..2....0..3..1..4..1..1....2..1..4..1..2..0....1..4..1..1..0..1
..1..3..2..1..0..1....2..1..4..1..0..1....1..0..1..1..3..1....0..1..2..3..1..2
..2..1..0..2..1..2....1..0..1..3..1..2....2..1..1..0..1..2....1..2..0..1..2..0

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

A197249 Number of nX7 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,0,1,1,1 for x=0,1,2,3,4.

Original entry on oeis.org

2, 192, 1035, 16773, 213912, 3264225, 48703999, 692974749, 9613268927, 144634486646, 2038308764828, 29317910548935, 416838295672468, 6110472912181664, 87970427980764925, 1247341042216025997

Offset: 1

R. H. Hardin Oct 12 2011

nonn

Every 0 is next to 0 0's, every 1 is next to 1 0's, every 2 is next to 2 1's, every 3 is next to 3 1's, every 4 is next to 4 1's

Column 7 of A197250

			Some solutions containing all values 0 to 4 for n=4
..1..2..0..1..1..2..0....0..2..1..0..1..1..2....2..1..2..2..1..2..0
..0..1..3..1..0..1..1....2..1..4..1..2..0..1....1..0..1..1..0..1..1
..1..4..1..4..1..1..3....1..0..1..1..3..1..2....1..1..3..2..1..4..1
..2..1..0..1..2..0..1....2..1..1..0..1..2..0....0..2..1..0..1..1..0

R. H. Hardin, Table of n, a(n) for n = 1..155

A197243 Number of n X n 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 0,0,1,1,1 for x=0,1,2,3,4.

Original entry on oeis.org

1, 4, 3, 275, 5062, 405065, 48703999, 11304892092, 9455531359836, 13086658688226332

Offset: 1

R. H. Hardin Oct 12 2011

nonn

Every 0 is next to 0 0's, every 1 is next to 1 0's, every 2 is next to 2 1's, every 3 is next to 3 1's, every 4 is next to 4 1's

Diagonal of A197250

			All solutions containing all values 0 to 4 for n=4
..0..1..3..1....1..0..1..2....1..3..1..0....2..1..0..1
..1..4..1..0....3..1..4..1....0..1..4..1....1..4..1..3
..3..1..4..1....1..4..1..0....1..4..1..3....0..1..4..1
..1..0..1..2....0..1..3..1....2..1..0..1....1..3..1..0

cp's OEIS Frontend

A197244 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,0,1,1,1 for x=0,1,2,3,4.

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A197245 Number of nX3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,0,1,1,1 for x=0,1,2,3,4.

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A197246 Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,0,1,1,1 for x=0,1,2,3,4.

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A197247 Number of nX5 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,0,1,1,1 for x=0,1,2,3,4.

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A197248 Number of nX6 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,0,1,1,1 for x=0,1,2,3,4.

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A197249 Number of nX7 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,0,1,1,1 for x=0,1,2,3,4.

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A197243 Number of n X n 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 0,0,1,1,1 for x=0,1,2,3,4.

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