A343095 -id:A343095 - cp's OEIS frontend

A047941 Number of 6-colorings of an n X n grid, up to rotational symmetry.

1, 6, 336, 2521476, 705277897416, 7107572010747738816, 2578606199622659276537193216, 33678386561031835867238388699701784576, 15835071665743319426540573726368249140484891508736, 268034865369025581797148715934176748584236925114472848300179456

Offset: 0

Rob Pratt

nonn

Andrew Howroyd, Table of n, a(n) for n = 0..25

Column k=6 of A343095.

Cf. A047937.

a(n) = (m^(n^2) + 2 m^((n^2 + 3 (n mod 2))/4) + m^((n^2 + (n mod 2))/2))/4, with m = 6.

Terms a(9) and beyond from Andrew Howroyd, Apr 14 2021

A047942 Number of 7-colorings of an n X n grid, up to rotational symmetry.

Original entry on oeis.org

1, 7, 616, 10092775, 8308234084801, 335267154940213889575, 662932711464913775048175499816, 64230894380264719522488136461023341060807, 304940121908958925034643465916849873749900601574419201, 70938377295002676956115265690779190293441720530070400876280330568007

Offset: 0

Rob Pratt

nonn

Andrew Howroyd, Table of n, a(n) for n = 0..25

Column k=7 of A343095.

Cf. A047937.

a(n) = (m^(n^2) + 2 m^((n^2 + 3 (n mod 2))/4) + m^((n^2 + (n mod 2))/2))/4, with m = 7.

Terms a(8) and beyond from Andrew Howroyd, Apr 14 2021

A047943 Number of 8-colorings of an n X n grid, up to rotational symmetry.

Original entry on oeis.org

1, 8, 1044, 33562880, 70368748374016, 9444732965876730429440, 81129638414606686199388699623424, 44601490397061246283080881278262737180295168, 1569275433846670190958947355821723644654155086251882971136

Offset: 0

Rob Pratt

nonn

Andrew Howroyd, Table of n, a(n) for n = 0..25

Column k=8 of A343095.

Cf. A047937.

a(n) = (m^(n^2) + 2 m^((n^2 + 3 (n mod 2))/4) + m^((n^2 + (n mod 2))/2))/4, with m = 8.

Terms a(8) and beyond from Andrew Howroyd, Apr 14 2021

A047944 Number of 9-colorings of an n X n grid, up to rotational symmetry.

Original entry on oeis.org

1, 9, 1665, 96870249, 463255057977921, 179474496923598616041129, 5632099886234793640483695986653185, 14316042242555870306568544190208626253583093449, 2947546144434645792880218215353988087374626027116634833972481

Offset: 0

Rob Pratt

nonn

Andrew Howroyd, Table of n, a(n) for n = 0..25

Column k=9 of A343095.

Cf. A047937.

a(n) = (m^(n^2) + 2 m^((n^2 + 3 (n mod 2))/4) + m^((n^2 + (n mod 2))/2))/4, with m = 9.

Terms a(8) and beyond from Andrew Howroyd, Apr 14 2021

A047945 Number of 10-colorings of an n X n grid, up to rotational symmetry.

Original entry on oeis.org

1, 10, 2530, 250025500, 2500000025005000, 2500000000002500005000000, 250000000000000000250000000500000000, 2500000000000000000000002500000000005000000000000, 2500000000000000000000000000000025000000000000005000000000000000

Offset: 0

Rob Pratt

nonn

Andrew Howroyd, Table of n, a(n) for n = 0..25

Column k=10 of A343095.

Cf. A047937.

a(n) = (m^(n^2) + 2 m^((n^2 + 3 (n mod 2))/4) + m^((n^2 + (n mod 2))/2))/4, with m = 10.

Terms a(8) and beyond from Andrew Howroyd, Apr 14 2021

A343096 Number of n-colorings of an n X n grid, up to rotational symmetry.

Original entry on oeis.org

1, 1, 6, 4995, 1073758336, 74505806274453125, 2578606199622659276537193216, 64230894380264719522488136461023341060807, 1569275433846670190958947355821723644654155086251882971136, 49156762618888228404518977131728029071108432602235970059344750602021716398409

Offset: 0

Andrew Howroyd, Apr 14 2021

nonn

Andrew Howroyd, Table of n, a(n) for n = 0..25
Peter Kagey and William Keehn, Counting Tilings of the n X m Grid, Cylinder, and Torus, J. Int. Seq. (2024) Vol. 27, Art. No. 24.6.1. See p. 2.

Main diagonal of A343095.

Cf. A002489.

a:= n-> (n^(n^2)+2*n^((n^2+3*(n mod 2))/4)+n^((n^2+(n mod 2))/2))/4:
seq(a(n), n=0..10);  # Alois P. Heinz, May 12 2021

a(n) = {(n^(n^2) + 2*n^((n^2 + 3*(n%2))/4) + n^((n^2 + (n%2))/2))/4}

a(n) = (n^(n^2) + 2*n^((n^2 + 3*(n mod 2))/4) + n^((n^2 + (n mod 2))/2))/4.

cp's OEIS Frontend

A047941 Number of 6-colorings of an n X n grid, up to rotational symmetry.

Views

Author

Keywords

Links

Crossrefs

Formula

Extensions

A047942 Number of 7-colorings of an n X n grid, up to rotational symmetry.

Views

Author

Keywords

Links

Crossrefs

Formula

Extensions

A047943 Number of 8-colorings of an n X n grid, up to rotational symmetry.

Views

Author

Keywords

Links

Crossrefs

Formula

Extensions

A047944 Number of 9-colorings of an n X n grid, up to rotational symmetry.

Views

Author

Keywords

Links

Crossrefs

Formula

Extensions

A047945 Number of 10-colorings of an n X n grid, up to rotational symmetry.

Views

Author

Keywords

Links

Crossrefs

Formula

Extensions

A343096 Number of n-colorings of an n X n grid, up to rotational symmetry.

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

PARI

Formula