A197280 -id:A197280 - cp's OEIS frontend

A197274 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,1,1,1 for x=0,1,2,3,4.

3, 9, 14, 29, 67, 134, 275, 583, 1210, 2511, 5245, 10926, 22745, 47405, 98774, 205765, 428731, 893294, 1861163, 3877815, 8079642, 16834247, 35074949, 73080470, 152266769, 317255517, 661018310, 1377265789, 2869604691, 5978971062

Offset: 1

R. H. Hardin, Oct 12 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 1's, every 4 is next to 4 1's.

Column 2 of A197280.

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

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

Cf. A197280.

Empirical: a(n) = 2*a(n-1) +2*a(n-3) -2*a(n-4) -2*a(n-5) -a(n-6) -2*a(n-7).

Empirical g.f.: (1 + x)^2*(3 - 3*x - x^2 - 2*x^4) / (1 - 2*x - 2*x^3 + 2*x^4 + 2*x^5 + x^6 + 2*x^7). - Colin Barker, May 11 2018

A197275 Number of nX3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,1,1,1 for x=0,1,2,3,4.

Original entry on oeis.org

4, 14, 34, 92, 317, 888, 2626, 8078, 24103, 72107, 217970, 656610, 1975147, 5955136, 17950843, 54086244, 163025795, 491430743, 1481229421, 4464844849, 13458804609, 40569450638, 122290929298, 368632726282, 1111201586358, 3349591968789

Offset: 1

R. H. Hardin Oct 12 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 1's, every 4 is next to 4 1's

Column 3 of A197280

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

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

Empirical: a(n) = 3*a(n-1) +a(n-2) -6*a(n-4) -11*a(n-5) +19*a(n-6) -13*a(n-7) -64*a(n-8) +21*a(n-9) +36*a(n-10) -8*a(n-11) -93*a(n-12) +28*a(n-13) -52*a(n-14) -11*a(n-15) +27*a(n-16) -16*a(n-17) -a(n-18) +3*a(n-19)

A197276 Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,1,1,1 for x=0,1,2,3,4.

Original entry on oeis.org

5, 29, 92, 627, 2731, 11850, 57137, 276689, 1344992, 6445595, 30716245, 146763830, 705198523, 3392533967, 16288546542, 78114416927, 374644274789, 1797996141058, 8631814710395, 41433944954559, 198846557512440, 954242657026897

Offset: 1

R. H. Hardin Oct 12 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 1's, every 4 is next to 4 1's

Column 4 of A197280

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

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

Empirical: a(n) = 5*a(n-1) -4*a(n-2) +13*a(n-3) +24*a(n-4) +130*a(n-5) -534*a(n-6) -1467*a(n-7) -4061*a(n-8) -350*a(n-9) +660*a(n-10) +17309*a(n-11) +66603*a(n-12) +88830*a(n-13) +151269*a(n-14) +969572*a(n-15) +2151806*a(n-16) +3042232*a(n-17) +1395300*a(n-18) -2383750*a(n-19) -8156803*a(n-20) -13461098*a(n-21) -10627875*a(n-22) -2467733*a(n-23) +13987981*a(n-24) +20501622*a(n-25) +28114422*a(n-26) +30220361*a(n-27) +26876503*a(n-28) +11999640*a(n-29) -818003*a(n-30) +2977612*a(n-31) -6343090*a(n-32) -13797361*a(n-33) -12922199*a(n-34) -10283694*a(n-35) -4953615*a(n-36) -6395186*a(n-37) -4561904*a(n-38) -233451*a(n-39) -791355*a(n-40) -868034*a(n-41) -308312*a(n-42) -248750*a(n-43) +8267*a(n-44) +48879*a(n-45) -5430*a(n-46) -9498*a(n-47) -9755*a(n-48) -3296*a(n-49) -698*a(n-50) +3*a(n-51) +40*a(n-52) +2*a(n-53)

A197277 Number of nX5 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,1,1,1 for x=0,1,2,3,4.

Original entry on oeis.org

9, 67, 317, 2731, 16890, 114205, 886737, 6017949, 40918349, 290053910, 2074566978, 14599100959, 101671464178, 714232555115, 5052846176923, 35608078988237, 249861298059545, 1755724243450685, 12370064599008231, 87120870560445460

Offset: 1

R. H. Hardin Oct 12 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 1's, every 4 is next to 4 1's

Column 5 of A197280

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

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

A197278 Number of n X 6 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,1,1,1 for x=0,1,2,3,4.

Original entry on oeis.org

16, 134, 888, 11850, 114205, 1276986, 13500114, 135563958, 1464662469, 15975572837, 167590942240, 1768832921236, 19029812782209, 203511535493020, 2157669619156227, 22971322152723986, 245668877166018309, 2619846491701562613, 27883612518177103171, 297316240949616974969

Offset: 1

R. H. Hardin, Oct 12 2011

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 1's, every 4 is next to 4 1's

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

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

Column 6 of A197280.

A197279 Number of nX7 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,1,1,1 for x=0,1,2,3,4.

Original entry on oeis.org

25, 275, 2626, 57137, 886737, 13500114, 209785488, 3332948197, 55701159000, 888511016495, 14113426224907, 227682122103328, 3670040705518361, 58842498077190676, 948189035889733725, 15294961470395061151

Offset: 1

R. H. Hardin Oct 12 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 1's, every 4 is next to 4 1's

Column 7 of A197280

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

R. H. Hardin, Table of n, a(n) for n = 1..118

A197273 Number of n X n 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 2,0,1,1,1 for x=0,1,2,3,4.

Original entry on oeis.org

1, 9, 34, 627, 16890, 1276986, 209785488, 84453386767, 71088592371829

Offset: 1

R. H. Hardin Oct 12 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 1's, every 4 is next to 4 1's

Diagonal of A197280

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

cp's OEIS Frontend

A197274 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,1,1,1 for x=0,1,2,3,4.

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A197275 Number of nX3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,1,1,1 for x=0,1,2,3,4.

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A197276 Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,1,1,1 for x=0,1,2,3,4.

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A197277 Number of nX5 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,1,1,1 for x=0,1,2,3,4.

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A197278 Number of n X 6 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,1,1,1 for x=0,1,2,3,4.

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A197279 Number of nX7 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,1,1,1 for x=0,1,2,3,4.

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A197273 Number of n X n 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 2,0,1,1,1 for x=0,1,2,3,4.

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