cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Previous Showing 21-28 of 28 results.

A068265 1/15 the number of colorings of an n X n square array with 15 colors.

Original entry on oeis.org

1, 2562, 1121513134, 83883341208384732, 1071996076636962150571633386, 2340759471154169773945494478241264553960, 873306114650864371018759651512626175923988398193371716, 55670142239312854542084127479622099015674204276236803402441613218850844
Offset: 1

Views

Author

R. H. Hardin, Feb 24 2002

Keywords

Crossrefs

Extensions

a(5)-a(8) from Alois P. Heinz, Apr 27 2012

A068266 1/16 the number of colorings of an n X n square array with 16 colors.

Original entry on oeis.org

1, 3165, 1982119455, 245622604880564955, 6022672393066051875922651155, 29220829891835424567142114269163936868895, 28052931461360411640129365206060753190589761972840149815, 5329007775881376959796836954274567596610268811025721999774999394622215355
Offset: 1

Views

Author

R. H. Hardin, Feb 24 2002

Keywords

Crossrefs

Extensions

a(5)-a(8) from Alois P. Heinz, Apr 27 2012

A068267 1/17 the number of colorings of an n X n square array with 17 colors.

Original entry on oeis.org

1, 3856, 3373402576, 669566077899139456, 30151771791510037597255660816, 308053647651282803104693654675496996201056, 714058835879284684324470416584413995932326192121670240896, 375522326791659350740130359662485880296223549591107434149113597657567050816
Offset: 1

Views

Author

R. H. Hardin, Feb 24 2002

Keywords

Crossrefs

Extensions

a(5)-a(8) from Alois P. Heinz, Apr 27 2012

A068268 1/18 the number of colorings of an n X n square array with 18 colors.

Original entry on oeis.org

1, 4641, 5554571857, 1714419367669298289, 136461767759964622690609683537, 2801124263786734144622842493797034683405617, 14827953377838619886793709359009173477911476430325930106481, 20242190237452646688395985657256161903754274932459524235140863308223305109841
Offset: 1

Views

Author

R. H. Hardin, Feb 24 2002

Keywords

Crossrefs

Extensions

a(5)-a(8) from Alois P. Heinz, Apr 27 2012

A068269 1/19 the number of colorings of an n X n square array with 19 colors.

Original entry on oeis.org

1, 5526, 8882874018, 4153630571837864748, 564981170863476314096512687566, 22354853275061169487985050625489956484533056, 257300965334378745090532920060644632998190650709754736514068, 861475141050998806961235302195978945049151803599433480523424276423626596675468
Offset: 1

Views

Author

R. H. Hardin, Feb 24 2002

Keywords

Crossrefs

Extensions

a(5)-a(8) from Alois P. Heinz, Apr 27 2012

A068270 1/20 the number of colorings of an n X n square array with 20 colors.

Original entry on oeis.org

1, 6517, 13841287219, 9580458187250990407, 2161111220298293067819628379911, 158872597397775739573835110149847235229271675, 3806290340846629510463844992746098005507806101928649895595171, 29719114772241665792629546781476756531800106771541628945462624575440369135473679
Offset: 1

Views

Author

R. H. Hardin, Feb 24 2002

Keywords

Crossrefs

Extensions

a(5)-a(8) from Alois P. Heinz, Apr 27 2012

A277443 Square array A(n,k) (n>=1, k>=1) read by antidiagonals: A(n,k) is the number of n-colorings of the prism graph Y_k on 2k vertices.

Original entry on oeis.org

0, 0, 0, 0, 2, 0, 0, 0, 18, 0, 0, 2, 12, 84, 0, 0, 0, 114, 264, 260, 0, 0, 2, 180, 2652, 1920, 630, 0, 0, 0, 858, 16080, 29660, 8520, 1302, 0, 0, 2, 1932, 119844, 367080, 198030, 28140, 2408, 0, 0, 0, 7074, 816984, 4843460, 4067280, 932862, 76272, 4104, 0, 0, 2, 18660, 5784492, 62682480, 85847910, 28576380, 3440024, 179424, 6570, 0
Offset: 1

Views

Author

Jeremy Tan, Oct 15 2016

Keywords

Comments

Y_1 contains a loop, so has no colorings with any number of colors. Y_2 is the cycle graph C_4 with two double edges; these two graphs are therefore equivalent with respect to number of colorings.

Examples

			Square array A(n,k) begins:
  0,   0,    0,      0,       0,        0,          0, ...
  0,   2,    0,      2,       0,        2,          0, ...
  0,  18,   12,    114,     180,      858,       1932, ...
  0,  84,  264,   2652,   16080,   119844,     816984, ...
  0, 260, 1920,  29660,  367080,  4843460,   62682480, ...
  0, 630, 8520, 198030, 4067280, 85847910, 1800687000, ...
		

Crossrefs

Cf. A277444 (colorings of Möbius ladders), A182406 (square grid graphs).
Columns k=1,2 are A000004 and A091940.
Rows n=1,2 are A000004 and A010673.

Formula

A(n,k) = (n^2-3n+3)^k+(n-1)((3-n)^k+(1-n)^k)+n^2-3n+1.

A277444 Square array A(n,k) (n>=1, k>=1) read by antidiagonals: A(n,k) is the number of n-colorings of the Möbius ladder M_k on 2k vertices.

Original entry on oeis.org

0, 0, 2, 0, 0, 6, 0, 2, 0, 12, 0, 0, 42, 24, 20, 0, 2, 48, 420, 120, 30, 0, 0, 306, 2160, 2420, 360, 42, 0, 2, 600, 17532, 27600, 9750, 840, 56, 0, 0, 2442, 115464, 375260, 191760, 30702, 1680, 72, 0, 2, 6048, 830100, 4810680, 4098510, 917280, 81032, 3024, 90, 0, 0, 20706, 5745120, 62813540, 85691640, 28669662, 3406368, 187560, 5040, 110
Offset: 1

Views

Author

Jeremy Tan, Oct 15 2016

Keywords

Comments

M_1 is two vertices connected by a triple edge and thus behaves like the path graph P_2 in terms of colorings. M_2 is isomorphic to K_4, the tetrahedral graph.

Examples

			Square array A(n,k) begins:
0,    0,    0,      0,       0,        0,          0, ...
2,    0,    2,      0,       2,        0,          2, ...
6,    0,   42,     48,     306,      600,       2442, ...
12,  24,  420,   2160,   17532,   115464,     830100, ...
20, 120, 2420,  27600,  375260,  4810680,   62813540, ...
30, 360, 9750, 191760, 4098510, 85691640, 1801468230, ...
		

Crossrefs

Cf. A277443 (colorings of prism graphs), A182406 (square grid graphs).
Columns k=1,2 are A002378 and A052762. Rows n=1,2 are A000004 and A010673.

Formula

A(n,k) = (n^2-3n+3)^k+(n-1)((3-n)^k-(1-n)^k)-1.
Previous Showing 21-28 of 28 results.