A197537 -id:A197537 - cp's OEIS frontend

A197531 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,1,0,0 for x=0,1,2,3,4.

3, 9, 16, 33, 73, 160, 361, 835, 1966, 4703, 11399, 27914, 68903, 171121, 426940, 1068865, 2682789, 6746336, 16988333, 42822747, 108024178, 272648551, 688426371, 1738750602, 4392467427, 11098043841, 28043540864, 70868720569, 179102669081

Offset: 1

R. H. Hardin, Oct 16 2011

nonn

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

Column 2 of A197537.

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

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

Cf. A197537.

Empirical: a(n) = 3*a(n-1) - a(n-3) - 4*a(n-4) - 3*a(n-5) + a(n-7) + a(n-8).

Empirical g.f.: x*(1 + x)^2*(3 - 6*x - 2*x^2 - 2*x^3 + x^4 + 2*x^5) / ((1 - x - x^2 - x^3)*(1 - 2*x - x^2 - x^3 + x^5)). - Colin Barker, Mar 02 2018

A197532 Number of nX3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,1,0,0 for x=0,1,2,3,4.

Original entry on oeis.org

4, 16, 56, 216, 868, 3500, 14085, 56842, 229706, 928664, 3755722, 15191220, 61451640, 248596817, 1005703793, 4068662528, 16460279703, 66592450774, 269410213656, 1089943115100, 4409547400430, 17839571907124, 72173035560719

Offset: 1

R. H. Hardin Oct 16 2011

nonn

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

Column 3 of A197537

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

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

Empirical: a(n) = 4*a(n-1) +5*a(n-2) -15*a(n-3) -21*a(n-4) +3*a(n-5) +28*a(n-6) +32*a(n-7) -5*a(n-8) -57*a(n-9) +10*a(n-10) +90*a(n-11) +44*a(n-12) -14*a(n-13) -101*a(n-14) -56*a(n-15) +46*a(n-16) +14*a(n-17) +11*a(n-18) -20*a(n-19) +9*a(n-20) +10*a(n-21) -9*a(n-22) -a(n-25)

A197533 Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,1,0,0 for x=0,1,2,3,4.

Original entry on oeis.org

5, 33, 216, 1419, 9373, 62586, 423085, 2879723, 19671764, 134643523, 922592723, 6325665762, 43386843099, 297644913045, 2042157812212, 14012277918367, 96148923597911, 659765081841360, 4527301927394765, 31066516652385893

Offset: 1

R. H. Hardin Oct 16 2011

nonn

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

Column 4 of A197537

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

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

Empirical: a(n) = 8*a(n-1) +4*a(n-2) -79*a(n-3) -30*a(n-4) +99*a(n-5) +41*a(n-6) +263*a(n-7) -405*a(n-8) +899*a(n-9) +7150*a(n-10) +6933*a(n-11) +8469*a(n-12) -2881*a(n-13) -45032*a(n-14) -44677*a(n-15) -82181*a(n-16) -77611*a(n-17) -25835*a(n-18) +35284*a(n-19) +242999*a(n-20) +361557*a(n-21) +412582*a(n-22) +192680*a(n-23) -167729*a(n-24) -442796*a(n-25) -480857*a(n-26) -373624*a(n-27) -111734*a(n-28) -57452*a(n-29) -25481*a(n-30) +186675*a(n-31) -47892*a(n-32) +194240*a(n-33) +243447*a(n-34) +94789*a(n-35) +253036*a(n-36) -22990*a(n-37) -5434*a(n-38) -112176*a(n-39) -176692*a(n-40) -20055*a(n-41) -59142*a(n-42) -41241*a(n-43) +34876*a(n-44) -30663*a(n-45) +12856*a(n-46) +1495*a(n-47) +26166*a(n-48) +13268*a(n-49) +10725*a(n-50) +8787*a(n-51) -4719*a(n-52) +2299*a(n-53) -1952*a(n-54) +414*a(n-55) +118*a(n-56) -729*a(n-57) -38*a(n-58) -281*a(n-59) -97*a(n-60) -73*a(n-61) -40*a(n-62) -34*a(n-63) -24*a(n-64) -8*a(n-65) -2*a(n-66)

A197534 Number of nX5 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,1,0,0 for x=0,1,2,3,4.

Original entry on oeis.org

9, 73, 868, 9373, 107655, 1220630, 14056707, 162042137, 1874230689, 21698542215, 251403042154, 2913819348602, 33779087426950, 391635814747885, 4540933400612193, 52653016886940873, 610534294176601038

Offset: 1

R. H. Hardin Oct 16 2011

nonn

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

Column 5 of A197537

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

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

A197535 Number of n X 6 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,1,0,0 for x=0,1,2,3,4.

Original entry on oeis.org

16, 160, 3500, 62586, 1220630, 23325250, 454280983, 8844380028, 172982554332, 3386294190736, 66356347688978, 1300795127521094, 25506585069158562, 500211695453958433, 9810478953775130079, 192417797960470740096

Offset: 1

R. H. Hardin, Oct 16 2011

nonn

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

Column 6 of A197537.

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

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

Cf. A197537.

A197536 Number of nX7 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,1,0,0 for x=0,1,2,3,4.

Original entry on oeis.org

25, 361, 14085, 423085, 14056707, 454280983, 14991391782, 493785636151, 16343961543732, 541269402906501, 17943273862788427, 595019891173209941, 19736497896904338854, 654726724059190203302, 21721092108797190824889

Offset: 1

R. H. Hardin Oct 16 2011

nonn

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

Column 7 of A197537

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

R. H. Hardin, Table of n, a(n) for n = 1..156

A197530 Number of n X n 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 2,0,1,0,0 for x=0,1,2,3,4.

Original entry on oeis.org

1, 9, 56, 1419, 107655, 23325250, 14991391782, 27504159228709, 145843735771766573

Offset: 1

R. H. Hardin Oct 16 2011

nonn

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

Diagonal of A197537

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

cp's OEIS Frontend

A197531 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,1,0,0 for x=0,1,2,3,4.

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A197532 Number of nX3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,1,0,0 for x=0,1,2,3,4.

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A197533 Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,1,0,0 for x=0,1,2,3,4.

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A197534 Number of nX5 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,1,0,0 for x=0,1,2,3,4.

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A197535 Number of n X 6 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,1,0,0 for x=0,1,2,3,4.

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A197536 Number of nX7 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,1,0,0 for x=0,1,2,3,4.

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A197530 Number of n X n 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 2,0,1,0,0 for x=0,1,2,3,4.

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