A196218 -id:A196218 - cp's OEIS frontend

A196212 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,1,2,4 for x=0,1,2,3,4.

3, 9, 20, 61, 189, 544, 1629, 4973, 15040, 45739, 140129, 429448, 1318027, 4054639, 12485046, 38469569, 118629261, 366006920, 1129623099, 3487480563, 10769378230, 33261326067, 102741225843, 317390237024, 980560274021, 3029559578685

Offset: 1

R. H. Hardin, Sep 29 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 2's, every 4 is next to 4 4's.

Column 2 of A196218.

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

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

Cf. A196218.

Empirical: a(n) = 2*a(n-1) +4*a(n-2) +6*a(n-3) -8*a(n-4) -39*a(n-5) -33*a(n-6) -17*a(n-7) +5*a(n-8) +8*a(n-9) +a(n-10).

Empirical g.f.: x*(1 + x)^2*(3 - 3*x - 7*x^2 - 16*x^3 - 4*x^4 + 15*x^5 + 3*x^6) / ((1 - x - 7*x^3 - x^4)*(1 - x - 5*x^2 - 4*x^3 - 2*x^4 + x^5 + x^6)). - Colin Barker, Feb 22 2018

A196213 Number of nX3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,1,2,4 for x=0,1,2,3,4.

Original entry on oeis.org

4, 20, 58, 290, 1217, 5110, 21969, 93666, 399920, 1714601, 7351903, 31469992, 134862960, 577985643, 2477090793, 10617586380, 45512098214, 195087643326, 836266725394, 3584843949857, 15367390560222, 65877090945921

Offset: 1

R. H. Hardin Sep 29 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 2's, every 4 is next to 4 4's

Column 3 of A196218

			Some solutions for n=4
..1..0..0....1..1..0....0..0..1....1..1..0....1..0..0....0..0..0....0..0..1
..1..2..1....0..1..1....1..1..1....0..1..2....2..2..1....1..1..1....1..1..2
..0..2..1....0..2..1....1..1..0....0..1..1....1..1..2....2..2..1....1..1..2
..1..1..0....0..0..0....0..2..1....1..1..0....0..0..0....1..0..0....0..0..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) +11*a(n-4) -62*a(n-5) -156*a(n-6) -641*a(n-7) -1661*a(n-8) -89*a(n-9) +1488*a(n-10) +10023*a(n-11) +43316*a(n-12) +46311*a(n-13) +45550*a(n-14) +21396*a(n-15) -79295*a(n-16) -76219*a(n-17) -105192*a(n-18) -56481*a(n-19) +54675*a(n-20) +38374*a(n-21) +65404*a(n-22) +5601*a(n-23) -13298*a(n-24) -5976*a(n-25) -4115*a(n-26) -1642*a(n-27) -2966*a(n-28) -1951*a(n-29) +693*a(n-30) +657*a(n-31) +83*a(n-32) +199*a(n-33) +48*a(n-34) -16*a(n-35) -3*a(n-36)

A196214 Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,1,2,4 for x=0,1,2,3,4.

Original entry on oeis.org

5, 61, 290, 2161, 14605, 101780, 723029, 5056631, 35105556, 245353935, 1720551401, 12056500808, 84351164429, 589889437285, 4128468776358, 28906652171595, 202358098703973, 1416223455876968, 9911711623472035, 69377533372430719

Offset: 1

R. H. Hardin Sep 29 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 2's, every 4 is next to 4 4's

Column 4 of A196218

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

R. H. Hardin, Table of n, a(n) for n = 1..250

A196215 Number of nX5 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,1,2,4 for x=0,1,2,3,4.

Original entry on oeis.org

9, 189, 1217, 14605, 173216, 1937895, 21716929, 244152037, 2771090244, 31410926798, 354585313303, 4007921508273, 45388862660525, 513791891452149, 5811758649045041, 65752943364665551, 744175679426127501

Offset: 1

R. H. Hardin Sep 29 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 2's, every 4 is next to 4 4's

Column 5 of A196218

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

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

A196216 Number of nX6 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,1,2,4 for x=0,1,2,3,4.

Original entry on oeis.org

16, 544, 5110, 101780, 1937895, 33962624, 608417005, 11132866106, 202301552532, 3661731514195, 66431113288877, 1207694877279204, 21927197259395828, 397962224047643681, 7227485386946689259, 131272592634933828858

Offset: 1

R. H. Hardin Sep 29 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 2's, every 4 is next to 4 4's

Column 6 of A196218

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

R. H. Hardin, Table of n, a(n) for n = 1..151

A196217 Number of nX7 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,1,2,4 for x=0,1,2,3,4.

Original entry on oeis.org

25, 1629, 21969, 723029, 21716929, 608417005, 17831030743, 525537881675, 15318916228421, 446553011295591, 13076767423341648, 382744483425525635, 11192520655926210678, 327413888234566814665, 9579556864719697800663

Offset: 1

R. H. Hardin Sep 29 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 2's, every 4 is next to 4 4's

Column 7 of A196218

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

R. H. Hardin, Table of n, a(n) for n = 1..45

A196211 Number of n X n 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 3,0,1,2,4 for x=0,1,2,3,4.

Original entry on oeis.org

1, 9, 58, 2161, 173216, 33962624, 17831030743, 24799094512239

Offset: 1

R. H. Hardin Sep 29 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 2's, every 4 is next to 4 4's

Diagonal of A196218

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

cp's OEIS Frontend

A196212 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,1,2,4 for x=0,1,2,3,4.

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A196213 Number of nX3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,1,2,4 for x=0,1,2,3,4.

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A196214 Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,1,2,4 for x=0,1,2,3,4.

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A196215 Number of nX5 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,1,2,4 for x=0,1,2,3,4.

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A196216 Number of nX6 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,1,2,4 for x=0,1,2,3,4.

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A196217 Number of nX7 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,1,2,4 for x=0,1,2,3,4.

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A196211 Number of n X n 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 3,0,1,2,4 for x=0,1,2,3,4.

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