A220177 -id:A220177 - cp's OEIS frontend

A220172 Sum of neighbor maps: number of n X 1 binary arrays indicating the locations of corresponding elements equal to the sum mod 3 of their horizontal, vertical and antidiagonal neighbors in a random 0..2 n X 1 array.

2, 2, 8, 16, 24, 64, 128, 232, 512, 1024, 1984, 4096, 8192, 16224, 32768, 65536, 130688, 262144, 524288, 1047680, 2097152, 4194304, 8386560, 16777216, 33554432, 67104256, 134217728, 268435456, 536860672, 1073741824, 2147483648, 4294944768

Offset: 1

R. H. Hardin, Dec 06 2012

nonn

Column 1 of A220177.

			All solutions for n=3:
..1....0....1....1....0....0....0....1
..1....1....0....1....0....0....1....0
..0....0....1....1....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-3) -8*a(n-4) -4*a(n-6) +8*a(n-7).

Empirical g.f.: 2*(1 - x + 2*x^2 - 4*x^3 + 4*x^6) / ((1 - 2*x)*(1 - 2*x^3)^2). - Colin Barker, Feb 18 2018

A220173 Sum of neighbor maps: number of nX2 binary arrays indicating the locations of corresponding elements equal to the sum mod 3 of their horizontal, vertical and antidiagonal neighbors in a random 0..2 nX2 array.

Original entry on oeis.org

2, 16, 48, 256, 856, 4096, 15872, 65536, 259584, 1048576, 4177632, 16777216, 67051520, 268435456, 1073479680, 4294967296, 17178580480, 68719476736, 274872664064, 1099511627776, 4398023442432, 17592186044416, 70368641459200

Offset: 1

R. H. Hardin Dec 06 2012

nonn

Column 2 of A220177

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

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

Empirical: a(n) = 4*a(n-1) +8*a(n-2) -32*a(n-3) -16*a(n-4) +64*a(n-5) +52*a(n-6) -208*a(n-7) -416*a(n-8) +1664*a(n-9) +832*a(n-10) -3328*a(n-11) -1056*a(n-12) +4224*a(n-13) +8448*a(n-14) -33792*a(n-15) -16896*a(n-16) +67584*a(n-17) +10880*a(n-18) -43520*a(n-19) -87040*a(n-20) +348160*a(n-21) +174080*a(n-22) -696320*a(n-23) -62720*a(n-24) +250880*a(n-25) +501760*a(n-26) -2007040*a(n-27) -1003520*a(n-28) +4014080*a(n-29) +205824*a(n-30) -823296*a(n-31) -1646592*a(n-32) +6586368*a(n-33) +3293184*a(n-34) -13172736*a(n-35) -360448*a(n-36) +1441792*a(n-37) +2883584*a(n-38) -11534336*a(n-39) -5767168*a(n-40) +23068672*a(n-41) +262144*a(n-42) -1048576*a(n-43) -2097152*a(n-44) +8388608*a(n-45) +4194304*a(n-46) -16777216*a(n-47)

A220174 Sum of neighbor maps: number of nX3 binary arrays indicating the locations of corresponding elements equal to the sum mod 3 of their horizontal, vertical and antidiagonal neighbors in a random 0..2 nX3 array.

Original entry on oeis.org

8, 48, 404, 4096, 31744, 262144, 2083808, 16728064, 134217728, 1073741824, 8586101128, 68719476736, 549755813888, 4397962625024, 35184307884032, 281474976710656, 2251796592459776, 18014398509481984, 144115183550922752

Offset: 1

R. H. Hardin Dec 06 2012

nonn

Column 3 of A220177

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

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

A220175 Sum of neighbor maps: number of nX4 binary arrays indicating the locations of corresponding elements equal to the sum mod 3 of their horizontal, vertical and antidiagonal neighbors in a random 0..2 nX4 array.

Original entry on oeis.org

16, 256, 4096, 65536, 1048576, 16777216, 268435456, 4294967296, 68701991383

Offset: 1

R. H. Hardin Dec 06 2012

nonn

Column 4 of A220177

a(n)=16^n for n<=8 but not for n=9

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

A220176 Sum of neighbor maps: number of nX5 binary arrays indicating the locations of corresponding elements equal to the sum mod 3 of their horizontal, vertical and antidiagonal neighbors in a random 0..2 nX5 array.

Original entry on oeis.org

24, 856, 31744, 1048576, 32395806, 1073741824, 34351349760

Offset: 1

R. H. Hardin Dec 06 2012

nonn

Column 5 of A220177

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

cp's OEIS Frontend

A220172 Sum of neighbor maps: number of n X 1 binary arrays indicating the locations of corresponding elements equal to the sum mod 3 of their horizontal, vertical and antidiagonal neighbors in a random 0..2 n X 1 array.

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A220173 Sum of neighbor maps: number of nX2 binary arrays indicating the locations of corresponding elements equal to the sum mod 3 of their horizontal, vertical and antidiagonal neighbors in a random 0..2 nX2 array.

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A220174 Sum of neighbor maps: number of nX3 binary arrays indicating the locations of corresponding elements equal to the sum mod 3 of their horizontal, vertical and antidiagonal neighbors in a random 0..2 nX3 array.

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A220175 Sum of neighbor maps: number of nX4 binary arrays indicating the locations of corresponding elements equal to the sum mod 3 of their horizontal, vertical and antidiagonal neighbors in a random 0..2 nX4 array.

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A220176 Sum of neighbor maps: number of nX5 binary arrays indicating the locations of corresponding elements equal to the sum mod 3 of their horizontal, vertical and antidiagonal neighbors in a random 0..2 nX5 array.

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