A222386 -id:A222386 - cp's OEIS frontend

A222381 Sum of neighbor maps: number of n X 2 binary arrays indicating the locations of corresponding elements equal to the sum mod 3 of their horizontal and antidiagonal neighbors in a random 0..2 n X 2 array.

2, 16, 64, 232, 1024, 4096, 16224, 65536, 262144, 1047680, 4194304, 16777216, 67104256, 268435456, 1073741824, 4294944768, 17179869184, 68719476736, 274877800448, 1099511627776, 4398046511104, 17592185552896, 70368744177664

Offset: 1

R. H. Hardin, Feb 18 2013

nonn

Column 2 of A222386.

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

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

Cf. A222386.

Empirical: a(n) = 4*a(n-1) + 8*a(n-3) - 32*a(n-4) - 16*a(n-6) + 64*a(n-7).

Empirical g.f.: 2*x*(1 + 4*x - 20*x^3 + 16*x^4 + 32*x^6) / ((1 - 4*x)*(1 - 4*x^3)^2). - Colin Barker, Mar 15 2018

A222382 Sum of neighbor maps: number of n X 3 binary arrays indicating the locations of corresponding elements equal to the sum mod 3 of their horizontal and antidiagonal neighbors in a random 0..2 n X 3 array.

Original entry on oeis.org

8, 48, 512, 3968, 32768, 261376, 2097152, 16773120, 134217728, 1073721344, 8589934592, 68719378432, 549755813888, 4398046052352, 35184372088832, 281474974613504, 2251799813685248, 18014398500044800, 144115188075855872

Offset: 1

R. H. Hardin, Feb 18 2013

nonn

Column 3 of A222386.

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

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

Cf. A222386.

Empirical: a(n) = 8*a(n-1) + 8*a(n-2) - 64*a(n-3) - 16*a(n-4) + 128*a(n-5).

Empirical g.f.: 8*x*(1 - 2*x + 8*x^2 + 16*x^4) / ((1 - 2*x)^2*(1 + 2*x)^2*(1 - 8*x)). - Colin Barker, Aug 16 2018

A222383 Sum of neighbor maps: number of nX4 binary arrays indicating the locations of corresponding elements equal to the sum mod 3 of their horizontal and antidiagonal neighbors in a random 0..2 nX4 array.

Original entry on oeis.org

16, 248, 3968, 63488, 1048320, 16777216, 268435072, 4294961152, 68702699520, 1099511597056, 17592186044416, 281474976700416, 4503599627206656, 72057490958712832, 1152921504603963392, 18446744073709551616

Offset: 1

R. H. Hardin Feb 18 2013

nonn

Column 4 of A222386

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

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

Empirical: a(n) = 16*a(n-1) +8352*a(n-5) -133632*a(n-6) -18096384*a(n-10) +289542144*a(n-11) +2753724416*a(n-15) -44059590656*a(n-16) -143077146624*a(n-20) +2289234345984*a(n-21) +2757369004032*a(n-25) -44117904064512*a(n-26) -17592186044416*a(n-30) +281474976710656*a(n-31)

A222384 Sum of neighbor maps: number of nX5 binary arrays indicating the locations of corresponding elements equal to the sum mod 3 of their horizontal and antidiagonal neighbors in a random 0..2 nX5 array.

Original entry on oeis.org

24, 1024, 32768, 1048576, 33546240, 1073741824, 34359738368, 1099510054912, 35184372088832, 1125899906842624, 36028796750528512, 1152921504606846976, 36893488147419103232, 1180591620674461630464, 37778931862957161709568

Offset: 1

R. H. Hardin Feb 18 2013

nonn

Column 5 of A222386

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

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

Empirical: a(n) = 32*a(n-1) +256*a(n-3) -8192*a(n-4) -16384*a(n-6) +524288*a(n-7) for n>9

A222385 Sum of neighbor maps: number of nX6 binary arrays indicating the locations of corresponding elements equal to the sum mod 3 of their horizontal and antidiagonal neighbors in a random 0..2 nX6 array.

Original entry on oeis.org

64, 3968, 262144, 16776896, 1073741712, 68719469568, 4398044807168, 281474968175508, 18014398509481984, 1152921504606846976, 73786976290732196864, 4722366482869645213696, 302231454903657058795520

Offset: 1

R. H. Hardin Feb 18 2013

nonn

Column 6 of A222386

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

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

A222387 Sum of neighbor maps: number of 2Xn binary arrays indicating the locations of corresponding elements equal to the sum mod 3 of their horizontal and antidiagonal neighbors in a random 0..2 2Xn array.

Original entry on oeis.org

4, 16, 48, 248, 1024, 3968, 15872, 65536, 262144, 1048576, 4177632, 16777216, 67108864, 268435456, 1073479680, 4294961152, 17179869184, 68719378432, 274872664064, 1099511627776, 4398046511104, 17592186044416, 70368641459200

Offset: 1

R. H. Hardin Feb 18 2013

nonn

Row 2 of A222386

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

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

Empirical: a(n) = 4*a(n-1) +32*a(n-4) -128*a(n-5) -256*a(n-8) +1024*a(n-9) +592*a(n-12) -2368*a(n-13) -18944*a(n-16) +75776*a(n-17) +151552*a(n-20) -606208*a(n-21) -109056*a(n-24) +436224*a(n-25) +3489792*a(n-28) -13959168*a(n-29) -27918336*a(n-32) +111673344*a(n-33) +6594560*a(n-36) -26378240*a(n-37) -211025920*a(n-40) +844103680*a(n-41) +1688207360*a(n-44) -6752829440*a(n-45) -189071360*a(n-48) +756285440*a(n-49) +6050283520*a(n-52) -24201134080*a(n-53) -48402268160*a(n-56) +193609072640*a(n-57) +2853175296*a(n-60) -11412701184*a(n-61) -91301609472*a(n-64) +365206437888*a(n-65) +730412875776*a(n-68) -2921651503104*a(n-69) -22011707392*a(n-72) +88046829568*a(n-73) +704374636544*a(n-76) -2817498546176*a(n-77) -5634997092352*a(n-80) +22539988369408*a(n-81) +68719476736*a(n-84) -274877906944*a(n-85) -2199023255552*a(n-88) +8796093022208*a(n-89) +17592186044416*a(n-92) -70368744177664*a(n-93)

A222388 Sum of neighbor maps: number of 3Xn binary arrays indicating the locations of corresponding elements equal to the sum mod 3 of their horizontal and antidiagonal neighbors in a random 0..2 3Xn array.

Original entry on oeis.org

8, 64, 512, 3968, 32768, 262144, 2093824, 16776064, 134121152, 1073741824, 8589934592, 68719450112, 549755703296, 4398040219648, 35184371580928, 281474867658752, 2251799813685248, 18014398509481984, 144115184855048192

Offset: 1

R. H. Hardin Feb 18 2013

nonn

Row 3 of A222386

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

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

A222389 Sum of neighbor maps: number of 4Xn binary arrays indicating the locations of corresponding elements equal to the sum mod 3 of their horizontal and antidiagonal neighbors in a random 0..2 4Xn array.

Original entry on oeis.org

16, 232, 3968, 63488, 1048576, 16776896, 268369920, 4294961152, 68702608704, 1099511627776, 17592160878592, 281474976700416, 4503599627370496

Offset: 1

R. H. Hardin Feb 18 2013

nonn

Row 4 of A222386

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

cp's OEIS Frontend

A222381 Sum of neighbor maps: number of n X 2 binary arrays indicating the locations of corresponding elements equal to the sum mod 3 of their horizontal and antidiagonal neighbors in a random 0..2 n X 2 array.

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A222382 Sum of neighbor maps: number of n X 3 binary arrays indicating the locations of corresponding elements equal to the sum mod 3 of their horizontal and antidiagonal neighbors in a random 0..2 n X 3 array.

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A222383 Sum of neighbor maps: number of nX4 binary arrays indicating the locations of corresponding elements equal to the sum mod 3 of their horizontal and antidiagonal neighbors in a random 0..2 nX4 array.

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A222384 Sum of neighbor maps: number of nX5 binary arrays indicating the locations of corresponding elements equal to the sum mod 3 of their horizontal and antidiagonal neighbors in a random 0..2 nX5 array.

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A222385 Sum of neighbor maps: number of nX6 binary arrays indicating the locations of corresponding elements equal to the sum mod 3 of their horizontal and antidiagonal neighbors in a random 0..2 nX6 array.

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A222387 Sum of neighbor maps: number of 2Xn binary arrays indicating the locations of corresponding elements equal to the sum mod 3 of their horizontal and antidiagonal neighbors in a random 0..2 2Xn array.

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A222388 Sum of neighbor maps: number of 3Xn binary arrays indicating the locations of corresponding elements equal to the sum mod 3 of their horizontal and antidiagonal neighbors in a random 0..2 3Xn array.

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A222389 Sum of neighbor maps: number of 4Xn binary arrays indicating the locations of corresponding elements equal to the sum mod 3 of their horizontal and antidiagonal neighbors in a random 0..2 4Xn array.

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