A198661 -id:A198661 - cp's OEIS frontend

A198655 Number of n X 1 0..7 arrays with values 0..7 introduced in row major order and each element equal to at least one horizontal or vertical neighbor.

0, 1, 1, 2, 3, 6, 11, 23, 47, 103, 226, 518, 1200, 2867, 6946, 17234, 43393, 111418, 290233, 768819, 2064637, 5626757, 15531220, 43432402, 122878654, 351665399, 1016952840, 2970387672, 8755225931, 26027153206, 77972236615, 235260594303

Offset: 1

R. H. Hardin, Oct 28 2011

nonn

Column 1 of A198661.

			All solutions for n=5:
..0....0....0
..0....0....0
..0....1....0
..0....1....1
..0....1....1

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

Cf. A198661.

Empirical: a(n) = 7*a(n-1) + a(n-2) - 97*a(n-3) + 105*a(n-4) + 531*a(n-5) - 757*a(n-6) - 1511*a(n-7) + 2143*a(n-8) + 2457*a(n-9) - 2689*a(n-10) - 2227*a(n-11) + 1198*a(n-12) + 840*a(n-13) for n>14.

Empirical g.f.: x^2*(1 - 6*x - 6*x^2 + 85*x^3 - 25*x^4 - 476*x^5 + 247*x^6 + 1348*x^7 - 523*x^8 - 1959*x^9 + 157*x^10 + 1157*x^11 + 309*x^12) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 - x - x^2)*(1 - x - 3*x^2)*(1 - x - 4*x^2)*(1 - x - 5*x^2)*(1 - x - 7*x^2)). - Colin Barker, Mar 02 2018

A198656 Number of nX2 0..7 arrays with values 0..7 introduced in row major order and each element equal to at least one horizontal or vertical neighbor.

Original entry on oeis.org

1, 3, 14, 76, 488, 3521, 28030, 242883, 2267306, 22621072, 239604079, 2677734762, 31381450817, 383270472363, 4847901589642, 63125725801101, 841517900517550, 11429291342102135, 157506922063918536, 2195111769933116471

Offset: 1

R. H. Hardin Oct 28 2011

nonn

Column 2 of A198661

			Some solutions with all values 0 to 7 for n=8
..0..0....0..0....0..1....0..0....0..0....0..1....0..1....0..1....0..0....0..0
..1..1....1..2....0..1....1..1....1..1....0..1....0..1....0..1....1..1....1..2
..2..2....1..2....2..3....2..2....2..2....2..2....2..2....2..2....2..2....1..2
..3..3....3..4....2..3....3..3....3..3....3..3....3..4....3..3....3..4....3..3
..4..5....3..4....4..5....4..4....4..4....4..5....3..4....4..4....3..4....4..4
..4..5....5..6....4..5....5..6....5..5....4..5....5..5....5..5....5..6....5..6
..6..7....5..6....6..7....5..6....6..6....6..7....6..7....6..6....5..6....5..6
..6..7....7..7....6..7....7..7....7..7....6..7....6..7....7..7....7..7....7..7

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

Empirical: a(n) = 50*a(n-1) -973*a(n-2) +8874*a(n-3) -29927*a(n-4) -92230*a(n-5) +939984*a(n-6) -1157338*a(n-7) -7025352*a(n-8) +14473974*a(n-9) +29278108*a(n-10) -54017762*a(n-11) -108264239*a(n-12) +78120984*a(n-13) +276328733*a(n-14) +56831952*a(n-15) -336850101*a(n-16) -307076936*a(n-17) +88644128*a(n-18) +275952224*a(n-19) +124163560*a(n-20) -45062112*a(n-21) -62248400*a(n-22) -20707200*a(n-23) -2210000*a(n-24)

A198657 Number of nX3 0..7 arrays with values 0..7 introduced in row major order and each element equal to at least one horizontal or vertical neighbor.

Original entry on oeis.org

1, 14, 185, 3904, 98467, 3053286, 109133049, 4460603630, 202661109307, 10057569576034, 533251017131222, 29684104738808241, 1708995821028336330, 100671800330158890680, 6020806089426293935506, 363687165160204642974491

Offset: 1

R. H. Hardin Oct 28 2011

nonn

Column 3 of A198661

			Some solutions with all values 0 to 7 for n=6
..0..0..1....0..1..1....0..1..1....0..1..2....0..0..1....0..1..1....0..1..1
..2..2..1....0..2..2....0..0..2....0..1..2....2..2..1....0..2..3....0..2..2
..3..4..5....3..3..4....3..3..2....3..3..4....3..3..4....0..2..3....3..3..2
..3..4..5....5..3..4....4..5..6....5..5..4....5..5..4....4..5..5....4..4..5
..6..6..0....5..6..7....4..5..6....6..6..6....6..6..4....4..6..6....6..5..5
..7..7..0....6..6..7....4..7..7....7..7..6....7..7..7....7..7..6....6..7..7

R. H. Hardin, Table of n, a(n) for n = 1..138

A198658 Number of nX4 0..7 arrays with values 0..7 introduced in row major order and each element equal to at least one horizontal or vertical neighbor.

Original entry on oeis.org

2, 76, 3904, 344044, 40065880, 6046334324, 1099981072751, 231069206905205, 53332894057280732, 13062771135606107106, 3312119561085281340968, 856694689962959996618514, 224079649012945587508397744

Offset: 1

R. H. Hardin Oct 28 2011

nonn

Column 4 of A198661

			Some solutions with all values 0 to 7 for n=4
..0..0..1..1....0..0..1..1....0..1..2..2....0..1..2..3....0..1..1..2
..2..2..3..4....2..2..3..4....0..1..3..3....0..1..2..3....0..3..3..2
..5..6..3..4....5..5..3..4....4..5..5..6....4..5..6..6....4..5..5..6
..5..6..7..7....6..6..7..7....4..7..7..6....4..5..7..7....4..7..7..6

R. H. Hardin, Table of n, a(n) for n = 1..17

A198659 Number of nX5 0..7 arrays with values 0..7 introduced in row major order and each element equal to at least one horizontal or vertical neighbor.

Original entry on oeis.org

3, 488, 98467, 40065880, 22693251873, 17510670291958

Offset: 1

R. H. Hardin Oct 28 2011

nonn

Column 5 of A198661

			Some solutions with all values 0 to 7 for n=4
..0..1..1..1..2....0..1..1..2..3....0..1..1..2..2....0..1..2..3..4
..0..2..3..4..2....0..4..1..2..3....0..3..3..2..0....0..1..2..3..4
..2..2..3..4..5....4..4..5..6..7....4..5..6..6..0....5..6..7..7..4
..6..6..7..7..5....2..2..5..6..7....4..5..5..7..7....5..6..7..3..3

A198660 Number of nX6 0..7 arrays with values 0..7 introduced in row major order and each element equal to at least one horizontal or vertical neighbor.

Original entry on oeis.org

6, 3521, 3053286, 6046334324, 17510670291958

Offset: 1

R. H. Hardin Oct 28 2011

nonn

Column 6 of A198661

			Some solutions with all values 0 to 7 for n=3
..0..0..1..2..3..4....0..0..1..1..2..2....0..0..1..1..2..3....0..1..2..2..3..3
..5..5..1..2..3..4....3..4..5..5..6..3....4..4..5..2..2..3....0..1..4..4..5..6
..5..6..6..7..7..4....3..4..7..7..6..3....6..6..5..5..7..7....7..7..0..0..5..6

cp's OEIS Frontend

A198655 Number of n X 1 0..7 arrays with values 0..7 introduced in row major order and each element equal to at least one horizontal or vertical neighbor.

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A198656 Number of nX2 0..7 arrays with values 0..7 introduced in row major order and each element equal to at least one horizontal or vertical neighbor.

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A198657 Number of nX3 0..7 arrays with values 0..7 introduced in row major order and each element equal to at least one horizontal or vertical neighbor.

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A198658 Number of nX4 0..7 arrays with values 0..7 introduced in row major order and each element equal to at least one horizontal or vertical neighbor.

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A198659 Number of nX5 0..7 arrays with values 0..7 introduced in row major order and each element equal to at least one horizontal or vertical neighbor.

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A198660 Number of nX6 0..7 arrays with values 0..7 introduced in row major order and each element equal to at least one horizontal or vertical neighbor.

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