A197317 -id:A197317 - cp's OEIS frontend

A197311 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,1,1,0,0 for x=0,1,2,3,4.

1, 0, 3, 2, 9, 6, 27, 18, 83, 56, 257, 176, 797, 556, 2475, 1766, 7699, 5640, 23995, 18106, 74937, 58408, 234541, 189266, 735771, 615834, 2313757, 2011340, 7294375, 6591454, 23056393, 21667064, 73073221, 71416640, 232226565, 235964308, 740061147

Offset: 1

R. H. Hardin, Oct 13 2011

nonn

Every 0 is next to 0 0's, every 1 is next to 1 1'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 A197317.

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

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

Cf. A197317.

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

Empirical g.f.: x*(1 - x - 3*x^2 + 5*x^3 - 2*x^4 - 7*x^5 + 6*x^6) / ((1 - 3*x^2)*(1 - x - 3*x^2 + 3*x^3 - x^5)). - Colin Barker, May 12 2018

A197312 Number of nX3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,1,1,0,0 for x=0,1,2,3,4.

Original entry on oeis.org

2, 3, 5, 10, 128, 79, 249, 662, 2767, 3969, 14343, 26565, 85744, 172877, 540761, 1086259, 3216870, 6970421, 19943621, 43866426, 122208464, 276719535, 753092637, 1739409216, 4652758432, 10905015671, 28759884710, 68307698666, 178118628885

Offset: 1

R. H. Hardin Oct 13 2011

nonn

Every 0 is next to 0 0's, every 1 is next to 1 1'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 A197317

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

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

Empirical: a(n) = 2*a(n-2) +3*a(n-3) +17*a(n-4) +a(n-5) +32*a(n-6) -13*a(n-7) -61*a(n-8) -41*a(n-9) -115*a(n-10) -83*a(n-11) -315*a(n-12) -280*a(n-13) -12*a(n-14) +214*a(n-15) -659*a(n-16) +358*a(n-17) +319*a(n-18) +247*a(n-19) -121*a(n-20) -109*a(n-21) -12*a(n-22) +50*a(n-23) +46*a(n-24) +a(n-25) -a(n-26) -3*a(n-27) for n>28

A197313 Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,1,1,0,0 for x=0,1,2,3,4.

Original entry on oeis.org

1, 2, 10, 160, 152, 790, 2724, 6242, 26422, 91756, 281296, 990140, 3437208, 11190922, 37836768, 129296206, 433975472, 1455029298, 4951850734, 16696765546, 56134653324, 190052231444, 641906625424, 2162290128232, 7306324921304

Offset: 1

R. H. Hardin Oct 13 2011

nonn

Every 0 is next to 0 0's, every 1 is next to 1 1'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 A197317

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

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

Empirical: a(n) = 2*a(n-1) +4*a(n-2) +6*a(n-3) -15*a(n-4) -14*a(n-5) +158*a(n-6) -75*a(n-7) -580*a(n-8) -544*a(n-9) +2442*a(n-10) -6108*a(n-11) -15674*a(n-12) +30424*a(n-13) +10460*a(n-14) -97388*a(n-15) +56218*a(n-16) +441502*a(n-17) -118178*a(n-18) -91784*a(n-19) +1837648*a(n-20) -170043*a(n-21) -3747640*a(n-22) -1924708*a(n-23) -22657*a(n-24) -7945855*a(n-25) -5336633*a(n-26) +10486980*a(n-27) +4002672*a(n-28) +5025718*a(n-29) +20403048*a(n-30) +11494725*a(n-31) +10614083*a(n-32) +10490910*a(n-33) +12687980*a(n-34) +9374913*a(n-35) -28487361*a(n-36) +8294976*a(n-37) +25580308*a(n-38) -60503291*a(n-39) -25248918*a(n-40) +13942686*a(n-41) -39639005*a(n-42) -37284559*a(n-43) -23466156*a(n-44) +22878562*a(n-45) +24899973*a(n-46) -31530561*a(n-47) +19180134*a(n-48) +36753693*a(n-49) -12016805*a(n-50) -3178342*a(n-51) +3297937*a(n-52) -4547374*a(n-53) +682965*a(n-54) -5465642*a(n-55) -4279697*a(n-56) +1150329*a(n-57) -2645817*a(n-58) +651720*a(n-59) +1143254*a(n-60) -684618*a(n-61) +266863*a(n-62) -143688*a(n-63) +60718*a(n-64) +108490*a(n-65) -45708*a(n-66) +14734*a(n-67) -10054*a(n-68) +2290*a(n-69) +1464*a(n-70) -1056*a(n-71) -16*a(n-72) -160*a(n-73) +48*a(n-74) for n>75

A197314 Number of nX5 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,1,1,0,0 for x=0,1,2,3,4.

Original entry on oeis.org

2, 9, 128, 152, 1033, 4780, 24903, 113774, 553807, 2751427, 13385323, 64601708, 318081207, 1550881210, 7598781154, 37018138503, 181198882339, 884596380240, 4326961466564, 21126289404408, 103287098681855, 504482396779592

Offset: 1

R. H. Hardin Oct 13 2011

nonn

Every 0 is next to 0 0's, every 1 is next to 1 1'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 A197317

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

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

A197315 Number of nX6 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,1,1,0,0 for x=0,1,2,3,4.

Original entry on oeis.org

4, 6, 79, 790, 4780, 24704, 189212, 1400102, 8813744, 62844698, 436492213, 3010736948, 20777197101, 144191070226, 998239321771, 6903357295660, 47811537748912, 330940337259970, 2291691748249353, 15860451380186238

Offset: 1

R. H. Hardin Oct 13 2011

nonn

Every 0 is next to 0 0's, every 1 is next to 1 1'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 A197317

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

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

A197316 Number of nX7 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,1,1,0,0 for x=0,1,2,3,4.

Original entry on oeis.org

2, 27, 249, 2724, 24903, 189212, 2241018, 20425821, 208960627, 1984221109, 20223402011, 195734767851, 1964217477394, 19163046359315, 191509608470344, 1875354477655910, 18682249962661264, 183413216662448071

Offset: 1

R. H. Hardin Oct 13 2011

nonn

Every 0 is next to 0 0's, every 1 is next to 1 1'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 A197317

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

R. H. Hardin, Table of n, a(n) for n = 1..109

A197310 Number of n X n 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 0,1,1,0,0 for x=0,1,2,3,4.

Original entry on oeis.org

1, 0, 5, 160, 1033, 24704, 2241018, 282284587, 82874179361

Offset: 1

R. H. Hardin Oct 13 2011

nonn

Every 0 is next to 0 0's, every 1 is next to 1 1'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 A197317

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

cp's OEIS Frontend

A197311 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,1,1,0,0 for x=0,1,2,3,4.

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A197312 Number of nX3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,1,1,0,0 for x=0,1,2,3,4.

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A197313 Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,1,1,0,0 for x=0,1,2,3,4.

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A197314 Number of nX5 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,1,1,0,0 for x=0,1,2,3,4.

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A197315 Number of nX6 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,1,1,0,0 for x=0,1,2,3,4.

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A197316 Number of nX7 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,1,1,0,0 for x=0,1,2,3,4.

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A197310 Number of n X n 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 0,1,1,0,0 for x=0,1,2,3,4.

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