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.

Showing 1-5 of 5 results.

A212039 Number of lower triangular n X n arrays colored with integers 0 upwards introduced in row major order, with no element equal to any element within a city block distance of two, and containing the value n(n+1)/2-2.

Original entry on oeis.org

0, 1, 4, 19, 58, 136, 271, 484, 799, 1243, 1846, 2641, 3664, 4954, 6553, 8506, 10861, 13669, 16984, 20863, 25366, 30556, 36499, 43264, 50923, 59551, 69226, 80029, 92044, 105358, 120061, 136246, 154009, 173449, 194668, 217771, 242866, 270064, 299479
Offset: 1

Views

Author

R. H. Hardin, Apr 28 2012

Keywords

Comments

Column 1 of A212044.

Examples

			Some solutions for n=4:
..0........0........0........0........0........0........0........0
..1.2......1.2......1.2......1.2......1.2......1.2......1.2......1.2
..3.4.5....3.4.5....3.4.5....3.4.5....3.4.1....3.4.5....3.4.5....3.4.5
..6.7.8.1..6.7.8.0..6.7.3.8..6.7.0.8..5.6.7.8..6.7.8.3..6.7.2.8..6.1.7.8
		

Crossrefs

Cf. A212044.

Formula

Empirical: a(n) = (1/8)*n^4 + (1/4)*n^3 - (25/8)*n^2 + (23/4)*n - 2 for n>1.
Conjectures from Colin Barker, Jul 20 2018: (Start)
G.f.: x^2*(1 - x + 9*x^2 - 7*x^3 + x^4) / (1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>6.
(End)

A212040 Number of lower triangular n X n arrays colored with integers 0 upwards introduced in row major order, with no element equal to any element within a city block distance of two, and containing the value n(n+1)/2-3.

Original entry on oeis.org

0, 1, 5, 119, 1310, 7849, 32696, 107400, 298404, 731960, 1630174, 3361016, 6505445, 11945114, 20974435, 35441099, 57919461, 91921515, 142150499, 214802485, 317921624, 461815031
Offset: 1

Views

Author

R. H. Hardin Apr 28 2012

Keywords

Comments

Column 2 of A212044

Examples

			Some solutions for n=4
..0........0........0........0........0........0........0........0
..1.2......1.2......1.2......1.2......1.2......1.2......1.2......1.2
..3.4.5....3.0.4....3.4.5....3.4.5....3.4.5....3.4.1....3.4.1....3.4.5
..6.0.7.1..5.6.7.3..6.1.7.4..5.0.6.7..6.0.7.2..5.6.7.0..5.6.7.4..6.0.7.6
		

Formula

Empirical: a(n) = (1/128)*n^8 + (1/32)*n^7 - (77/192)*n^6 - (3/16)*n^5 + (977/128)*n^4 - (1885/96)*n^3 + (1129/96)*n^2 + (355/24)*n - 15 for n>1

A212041 Number of lower triangular n X n arrays colored with integers 0 upwards introduced in row major order, with no element equal to any element within a city block distance of two, and containing the value n(n+1)/2-4.

Original entry on oeis.org

0, 0, 5, 319, 14949, 253072, 2326567, 14516200, 69305994, 271885024, 917364452, 2746402607, 7459357270
Offset: 1

Views

Author

R. H. Hardin Apr 28 2012

Keywords

Comments

Column 3 of A212044

Examples

			Some solutions for n=4
..0........0........0........0........0........0........0........0
..1.2......1.2......1.2......1.2......1.2......1.2......1.2......1.2
..3.0.4....3.4.5....3.4.1....3.4.0....3.0.4....3.4.5....3.4.5....3.0.4
..5.6.2.5..0.6.7.3..5.0.6.4..5.6.7.2..5.6.3.0..6.0.1.3..0.6.7.1..2.1.5.6
		

A212042 Number of lower triangular n X n arrays colored with integers 0 upwards introduced in row major order, with no element equal to any element within a city block distance of two, and containing the value n(n+1)/2-5.

Original entry on oeis.org

0, 0, 5, 447, 94131, 5054845, 109065807, 1339229741, 11235618109
Offset: 1

Views

Author

R. H. Hardin Apr 28 2012

Keywords

Comments

Column 4 of A212044

Examples

			Some solutions for n=4
..0........0........0........0........0........0........0........0
..1.2......1.2......1.2......1.2......1.2......1.2......1.2......1.2
..3.4.0....3.0.4....3.4.0....3.0.4....3.4.5....3.4.5....3.0.4....3.4.5
..0.5.3.4..5.1.2.5..5.6.3.5..5.6.7.5..5.0.6.2..2.1.0.2..5.1.6.2..6.7.2.1
		

A212043 Number of lower triangular n X n arrays colored with integers 0 upwards introduced in row major order, with no element equal to any element within a city block distance of two, and containing the value n(n+1)/2-6.

Original entry on oeis.org

0, 0, 5, 463, 339764, 65635205, 3564578765, 89579748909
Offset: 1

Views

Author

R. H. Hardin Apr 28 2012

Keywords

Comments

Column 5 of A212044

Examples

			Some solutions for n=4
..0........0........0........0........0........0........0........0
..1.2......1.2......1.2......1.2......1.2......1.2......1.2......1.2
..3.4.0....3.4.5....3.4.1....3.0.1....3.4.5....3.4.1....3.4.5....3.4.5
..0.5.6.2..5.6.7.8..5.0.3.6..2.4.5.0..2.6.0.4..5.6.3.5..0.6.3.4..6.0.7.3
		
Showing 1-5 of 5 results.