A198185 -id:A198185 - cp's OEIS frontend

A198179 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,2,1,0,0 for x=0,1,2,3,4.

0, 4, 3, 8, 16, 21, 56, 70, 171, 256, 516, 905, 1622, 3048, 5293, 9992, 17564, 32517, 58330, 106144, 192767, 348188, 634426, 1145535, 2084360, 3771658, 6847617, 12413706, 22507930, 40835531, 74015802, 134288434, 243440863, 441575714

Offset: 1

R. H. Hardin, Oct 21 2011

nonn

Every 0 is next to 0 0's, every 1 is next to 1 2'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 A198185.

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

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

Cf. A198185.

Empirical: a(n) = 3*a(n-2) +2*a(n-3) -2*a(n-4) -2*a(n-5) +4*a(n-7) -a(n-8) -3*a(n-9).

Empirical g.f.: x^2*(4 + 3*x - 4*x^2 - x^3 - x^4 + 6*x^5 - 3*x^6 - 7*x^7) / ((1 - x)*(1 + x - 2*x^2 - 4*x^3 - 2*x^4 - 4*x^7 - 3*x^8)). - Colin Barker, May 14 2018

A198180 Number of nX3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,2,1,0,0 for x=0,1,2,3,4.

Original entry on oeis.org

1, 3, 9, 25, 77, 148, 395, 866, 2346, 5663, 14065, 34309, 84252, 208413, 513352, 1266410, 3117377, 7679699, 18927327, 46639092, 114949605, 283220762, 697929906, 1719783577, 4237987789, 10443340285, 25734497336, 63415169957, 156267786924

Offset: 1

R. H. Hardin Oct 21 2011

nonn

Every 0 is next to 0 0's, every 1 is next to 1 2'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 A198185

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

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

Empirical: a(n) = a(n-1) +3*a(n-2) -a(n-3) +3*a(n-4) +14*a(n-5) -a(n-6) -13*a(n-7) -17*a(n-8) -43*a(n-9) -73*a(n-10) -111*a(n-11) -70*a(n-12) -49*a(n-13) +87*a(n-14) +274*a(n-15) +424*a(n-16) +337*a(n-17) +389*a(n-18) +202*a(n-19) +184*a(n-20) -420*a(n-21) -643*a(n-22) -580*a(n-23) -287*a(n-24) -116*a(n-25) -426*a(n-26) -5*a(n-27) +80*a(n-28) +414*a(n-29) +294*a(n-30) +24*a(n-31) -12*a(n-32) -72*a(n-33) -30*a(n-34) +4*a(n-36) +4*a(n-37)

A198181 Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,2,1,0,0 for x=0,1,2,3,4.

Original entry on oeis.org

2, 8, 25, 59, 331, 883, 3485, 12030, 43774, 155664, 540628, 1936313, 6871687, 24471790, 86551688, 306708029, 1089956129, 3870392120, 13733968845, 48703981505, 172844148554, 613561265167, 2177517194687, 7726401450405

Offset: 1

R. H. Hardin Oct 21 2011

nonn

Every 0 is next to 0 0's, every 1 is next to 1 2'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 A198185

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

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

A198182 Number of nX5 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,2,1,0,0 for x=0,1,2,3,4.

Original entry on oeis.org

1, 16, 77, 331, 2033, 8298, 48958, 216307, 1155412, 5522239, 28200527, 139401115, 695721892, 3477106364, 17307490471, 86498278609, 430707067503, 2150928384789, 10722364479972, 53497634923663, 266813770707004, 1330929200315097

Offset: 1

R. H. Hardin Oct 21 2011

nonn

Every 0 is next to 0 0's, every 1 is next to 1 2'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 A198185

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

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

A198183 Number of nX6 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,2,1,0,0 for x=0,1,2,3,4.

Original entry on oeis.org

1, 21, 148, 883, 8298, 51688, 395340, 2639341, 19059216, 135044844, 958174742, 6800519266, 48283678834, 342710822044, 2431565681788, 17263106688089, 122543913785532, 869732001977147, 6173405546650902, 43819646823646105

Offset: 1

R. H. Hardin Oct 21 2011

nonn

Every 0 is next to 0 0's, every 1 is next to 1 2'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 A198185

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

R. H. Hardin, Table of n, a(n) for n = 1..199

A198184 Number of nX7 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,2,1,0,0 for x=0,1,2,3,4.

Original entry on oeis.org

3, 56, 395, 3485, 48958, 395340, 4522496, 41084248, 441157382, 4292509761, 44051823241, 438360876506, 4438621935572, 44610898968447, 449562512780134, 4527350842044875, 45564682527974566, 459054827920170371

Offset: 1

R. H. Hardin Oct 21 2011

nonn

Every 0 is next to 0 0's, every 1 is next to 1 2'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 A198185

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

R. H. Hardin, Table of n, a(n) for n = 1..73

A198178 Number of n X n 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 0,2,1,0,0 for x=0,1,2,3,4.

Original entry on oeis.org

1, 4, 9, 59, 2033, 51688, 4522496, 559601114, 174674654015

Offset: 1

R. H. Hardin Oct 21 2011

nonn

Every 0 is next to 0 0's, every 1 is next to 1 2'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 A198185

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

cp's OEIS Frontend

A198179 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,2,1,0,0 for x=0,1,2,3,4.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A198180 Number of nX3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,2,1,0,0 for x=0,1,2,3,4.

Views

Author

Keywords

Comments

Examples

Links

Formula

A198181 Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,2,1,0,0 for x=0,1,2,3,4.

Views

Author

Keywords

Comments

Examples

Links

A198182 Number of nX5 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,2,1,0,0 for x=0,1,2,3,4.

Views

Author

Keywords

Comments

Examples

Links

A198183 Number of nX6 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,2,1,0,0 for x=0,1,2,3,4.

Views

Author

Keywords

Comments

Examples

Links

A198184 Number of nX7 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,2,1,0,0 for x=0,1,2,3,4.

Views

Author

Keywords

Comments

Examples

Links

A198178 Number of n X n 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 0,2,1,0,0 for x=0,1,2,3,4.

Views

Author

Keywords

Comments

Examples