A068248 -id:A068248 - cp's OEIS frontend

A068761 Number of potential flows in n X n array with integer velocities in -14..14, i.e., number of n X n arrays with adjacent elements differing by no more than 14, counting arrays differing by a constant only once.

Original entry on oeis.org

1, 16269, 105227044417, 278175212679968120043

Offset: 1

R. H. Hardin, Feb 27 2002

nonn

By size 3 X 3, ..., 6 X 6 A068744-A068747, by velocity limit 1..14 A068248-A068761, solenoidal flows A068722-A068738.

A212195 Square array A(n,k), n>=1, k>=1, read by antidiagonals: A(n,k) is the number of n-colorings of the staggered hexagonal square grid graph SH_(k,k).

Original entry on oeis.org

1, 0, 2, 0, 0, 3, 0, 0, 6, 4, 0, 0, 6, 48, 5, 0, 0, 6, 1056, 180, 6, 0, 0, 6, 45696, 32940, 480, 7, 0, 0, 6, 4038432, 30847500, 393600, 1050, 8, 0, 0, 6, 743601024, 148046704020, 3312560640, 2735250, 2016, 9

Offset: 1

Alois P. Heinz, May 03 2012

The staggered hexagonal square grid graph SH_(n,n) has n^2 = A000290(n) vertices and (n-1)*(3*n-1) = A045944(n-1) edges; see A212194 for example. The chromatic polynomial of SH_(n,n) has n^2+1 = A002522(n) coefficients.

A differs from A212163 first at (n,k) = (4,5): A(4,5) = 4038432, A212163(4,5) = 4034304.

			Square array A(n,k) begins:
  1,    0,       0,            0,                 0, ...
  2,    0,       0,            0,                 0, ...
  3,    6,       6,            6,                 6, ...
  4,   48,    1056,        45696,           4038432, ...
  5,  180,   32940,     30847500,      148046704020, ...
  6,  480,  393600,   3312560640,   286170443437440, ...
  7, 1050, 2735250, 123791435250, 97337320223288250, ...

Wikipedia, Chromatic Polynomial

Columns k=1-6 give: A000027, A047927(n) = 6*A002417(n-2), 6*A068244, 6*A068245, 6*A068248, 6*A068249.
Rows n=1-10, 16-18 give: A000007, A000038, A040006, 4*A068283, 5*A068284, 6*A068285, 7*A068286, 8*A068287, 9*A068288, 10*A068289, 16*A068290, 17*A068291, 18*A068292.
Cf. A212163, A212194.

A068748 Number of potential flows in n X n array with integer velocities in -1..1, i.e., number of n X n arrays with adjacent elements differing by no more than 1, counting arrays differing by a constant only once.

Original entry on oeis.org

1, 19, 1665, 690437, 1366395515, 12961320464027, 590771311004409091, 129585582154154757804255, 136932044780329080616264070553, 697547669137459516115242710064880165

Offset: 1

R. H. Hardin, Feb 27 2002

nonn

By size 3 X 3, ..., 6 X 6 A068744-A068747, by velocity limit 1..14 A068248-A068761, solenoidal flows A068722-A068738.

A068752 Number of potential flows in n X n array with integer velocities in -5..5, i.e., number of n X n arrays with adjacent elements differing by no more than 5, counting arrays differing by a constant only once.

Original entry on oeis.org

1, 891, 45642289, 138190481342321, 24953087551680958151267

Offset: 1

R. H. Hardin, Feb 27 2002

nonn

By size 3 X 3, ..., 6 X 6 A068744-A068747, by velocity limit 1..14 A068248-A068761, A068752 solenoidal flows A068722-A068738.

A068749 Number of potential flows in n X n array with integer velocities in -2..2, i.e., number of n X n arrays with adjacent elements differing by no more than 2, counting arrays differing by a constant only once.

Original entry on oeis.org

1, 85, 87825, 1133641543, 184422574177355, 379827509377146575439, 9928923943603018785634645661

Offset: 1

R. H. Hardin, Feb 27 2002

nonn

By size 3 X 3, ..., 6 X 6 A068744-A068747, by velocity limit 1..14 A068248-A068761, solenoidal flows A068722-A068738.

A068750 Number of potential flows in n X n array with integer velocities in -3..3, i.e., number of n X n arrays with adjacent elements differing by no more than 3, counting arrays differing by a constant only once.

Original entry on oeis.org

1, 231, 1253329, 164185416899, 523957519578572209, 40918963843906494595507077

Offset: 1

R. H. Hardin, Feb 27 2002

nonn

By size 3 X 3, ..., 6 X 6 A068744-A068747, by velocity limit 1..14 A068248-A068761, solenoidal flows A068722-A068738.

A068751 Number of potential flows in n X n array with integer velocities in -4..4, i.e., number of n X n arrays with adjacent elements differing by no more than 4, counting arrays differing by a constant only once.

Original entry on oeis.org

1, 489, 9230193, 6913624013061, 207345516734034667209

Offset: 1

R. H. Hardin, Feb 27 2002

nonn

By size 3 X 3, ..., 6 X 6 A068744-A068747, by velocity limit 1..14 A068248-A068761, solenoidal flows A068722-A068738.

A068753 Number of potential flows in n X n array with integer velocities in -6..6, i.e., number of n X n arrays with adjacent elements differing by no more than 6, counting arrays differing by a constant only once.

Original entry on oeis.org

1, 1469, 172989921, 1678843050246451, 1354915464537160758459123

Offset: 1

R. H. Hardin, Feb 27 2002

nonn

By size 3 X 3, ..., 6 X 6 A068744-A068747, by velocity limit 1..14 A068248-A068761, solenoidal flows A068722-A068738.

A068754 Number of potential flows in n X n array with integer velocities in -7..7, i.e., number of n X n arrays with adjacent elements differing by no more than 7, counting arrays differing by a constant only once.

Original entry on oeis.org

1, 2255, 542131425, 14285299502131463

Offset: 1

R. H. Hardin, Feb 27 2002

nonn

By size 3 X 3, ..., 6 X 6 A068744-A068747, by velocity limit 1..14 A068248-A068761, solenoidal flows A068722-A068738.

A068755 Number of potential flows in n X n array with integer velocities in -8..8, i.e., number of n X n arrays with adjacent elements differing by no more than 8, counting arrays differing by a constant only once.

Original entry on oeis.org

1, 3281, 1473095713, 93044501704039945

Offset: 1

R. H. Hardin, Feb 27 2002

nonn

By size 3 X 3, ..., 6 X 6 A068744-A068747, by velocity limit 1..14 A068248-A068761, solenoidal flows A068722-A068738.

cp's OEIS Frontend

A068761 Number of potential flows in n X n array with integer velocities in -14..14, i.e., number of n X n arrays with adjacent elements differing by no more than 14, counting arrays differing by a constant only once.

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A212195 Square array A(n,k), n>=1, k>=1, read by antidiagonals: A(n,k) is the number of n-colorings of the staggered hexagonal square grid graph SH_(k,k).

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A068748 Number of potential flows in n X n array with integer velocities in -1..1, i.e., number of n X n arrays with adjacent elements differing by no more than 1, counting arrays differing by a constant only once.

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A068752 Number of potential flows in n X n array with integer velocities in -5..5, i.e., number of n X n arrays with adjacent elements differing by no more than 5, counting arrays differing by a constant only once.

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A068749 Number of potential flows in n X n array with integer velocities in -2..2, i.e., number of n X n arrays with adjacent elements differing by no more than 2, counting arrays differing by a constant only once.

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A068750 Number of potential flows in n X n array with integer velocities in -3..3, i.e., number of n X n arrays with adjacent elements differing by no more than 3, counting arrays differing by a constant only once.

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A068751 Number of potential flows in n X n array with integer velocities in -4..4, i.e., number of n X n arrays with adjacent elements differing by no more than 4, counting arrays differing by a constant only once.

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A068753 Number of potential flows in n X n array with integer velocities in -6..6, i.e., number of n X n arrays with adjacent elements differing by no more than 6, counting arrays differing by a constant only once.

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A068754 Number of potential flows in n X n array with integer velocities in -7..7, i.e., number of n X n arrays with adjacent elements differing by no more than 7, counting arrays differing by a constant only once.

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A068755 Number of potential flows in n X n array with integer velocities in -8..8, i.e., number of n X n arrays with adjacent elements differing by no more than 8, counting arrays differing by a constant only once.

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Author

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Crossrefs