A196300 -id:A196300 - cp's OEIS frontend

A196294 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,1,4,2 for x=0,1,2,3,4.

3, 9, 20, 61, 187, 536, 1597, 4849, 14582, 44097, 134349, 409428, 1249517, 3822519, 11705002, 35866253, 109991817, 337493970, 1035913925, 3180693901, 9768462112, 30005758115, 92181317503, 283222651372, 870256732085, 2674196289015

Offset: 1

R. H. Hardin, Sep 30 2011

nonn

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

Column 2 of A196300.

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

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

Cf. A196300.

Empirical: a(n) = 2*a(n-1) +4*a(n-2) +6*a(n-3) -9*a(n-4) -38*a(n-5) -32*a(n-6) -11*a(n-7) +6*a(n-8) +a(n-9).

Empirical g.f.: x*(1 + x)^2*(3 - 3*x - 7*x^2 - 16*x^3 - 3*x^4 + 15*x^5 + 2*x^6) / ((1 - x - 7*x^3 - x^4)*(1 - x - 5*x^2 - 4*x^3 - x^4 + x^5)). - Colin Barker, May 08 2018

A196295 Number of nX3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,1,4,2 for x=0,1,2,3,4.

Original entry on oeis.org

4, 20, 58, 290, 1201, 4988, 21344, 90150, 381754, 1621695, 6890299, 29235310, 124148208, 527208582, 2238746157, 9507860508, 40379986769, 171493157818, 728338492990, 3093321027043, 13137679999737, 55797480705949

Offset: 1

R. H. Hardin Sep 30 2011

nonn

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

Column 3 of A196300

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

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

Empirical: a(n) = 4*a(n-1) +3*a(n-2) -2*a(n-3) -3*a(n-4) -28*a(n-5) -108*a(n-6) -553*a(n-7) -1487*a(n-8) -406*a(n-9) +1679*a(n-10) +7367*a(n-11) +29776*a(n-12) +40461*a(n-13) +40921*a(n-14) +25939*a(n-15) +4942*a(n-16) -5887*a(n-17) -21877*a(n-18) -27360*a(n-19) -19016*a(n-20) +284*a(n-21) +3863*a(n-22) -2168*a(n-23) -3302*a(n-24) +3474*a(n-25) +1158*a(n-26) -171*a(n-27) -1312*a(n-28) +650*a(n-29) -96*a(n-30) +70*a(n-31) -18*a(n-32)

A196296 Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,1,4,2 for x=0,1,2,3,4.

Original entry on oeis.org

5, 61, 290, 2161, 14231, 97892, 686759, 4731033, 32374680, 222897413, 1539916243, 10636418118, 73345982967, 505430824497, 3485517910342, 24049220604349, 165913015451421, 1144300512605372, 7891941802463913, 54435005065152899

Offset: 1

R. H. Hardin Sep 30 2011

nonn

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

Column 4 of A196300

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

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

A196297 Number of nX5 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,1,4,2 for x=0,1,2,3,4.

Original entry on oeis.org

9, 187, 1201, 14231, 160800, 1752855, 19123802, 207927811, 2289816421, 25196042496, 275801202962, 3022047651617, 33191139932413, 364411328809394, 3997197786597231, 43850392251373127, 481263490991618506

Offset: 1

R. H. Hardin Sep 30 2011

nonn

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

Column 5 of A196300

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

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

A196298 Number of nX6 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,1,4,2 for x=0,1,2,3,4.

Original entry on oeis.org

16, 536, 4988, 97892, 1752855, 29726608, 513362648, 9011375854, 157499416616, 2741611675889, 47786154938133, 835079584650718, 14574818807228610, 254227577927404022, 4437435057747448441, 77465536560470518968

Offset: 1

R. H. Hardin Sep 30 2011

nonn

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

Column 6 of A196300

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

R. H. Hardin, Table of n, a(n) for n = 1..188

A196299 Number of nX7 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,1,4,2 for x=0,1,2,3,4.

Original entry on oeis.org

25, 1597, 21344, 686759, 19123802, 513362648, 14372583192, 402254701097, 11172616795189, 309961960884860, 8636593218691567, 240597854301944078, 6696378931249054755, 186420836116243663032, 5190804183327066922164

Offset: 1

R. H. Hardin Sep 30 2011

nonn

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

Column 7 of A196300

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

R. H. Hardin, Table of n, a(n) for n = 1..64

A196293 Number of n X n 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 3,0,1,4,2 for x=0,1,2,3,4.

Original entry on oeis.org

1, 9, 58, 2161, 160800, 29726608, 14372583192, 17833080104711

Offset: 1

R. H. Hardin Sep 30 2011

nonn

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

Diagonal of A196300

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

cp's OEIS Frontend

A196294 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,1,4,2 for x=0,1,2,3,4.

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A196295 Number of nX3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,1,4,2 for x=0,1,2,3,4.

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A196296 Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,1,4,2 for x=0,1,2,3,4.

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A196297 Number of nX5 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,1,4,2 for x=0,1,2,3,4.

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A196298 Number of nX6 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,1,4,2 for x=0,1,2,3,4.

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A196299 Number of nX7 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,1,4,2 for x=0,1,2,3,4.

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A196293 Number of n X n 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 3,0,1,4,2 for x=0,1,2,3,4.

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