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 1-4 of 4 results.

A265167 Number of n X 2 arrays containing 2 copies of 0..n-1 with no equal horizontal or vertical neighbors and new values introduced sequentially from 0.

Original entry on oeis.org

0, 1, 2, 21, 186, 2113, 27856, 422481, 7241480, 138478561, 2923183474, 67520866405, 1694065383154, 45878853274945, 1333966056696224, 41446945223914337, 1370476678395567376, 48051281596087884289
Offset: 1

Views

Author

R. H. Hardin, Dec 03 2015

Keywords

Comments

Column 2 of A265170.
a(n) is also the number of configurations of n indistinguishable pairs placed on the vertices of the ladder graph P_2 X P_n such that no such pair is joined by an edge; equivalently this is the number of "0-domino" configurations in the game of memory played on a 2 X n rectangular array, see [Young]. - Donovan Young, Oct 22 2018

Examples

			Some solutions for n=4
..0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1
..2..3....2..3....2..3....2..0....2..3....2..3....2..3....2..3....2..3....2..3
..0..1....3..2....0..2....1..3....0..1....3..0....3..1....1..2....3..2....0..2
..2..3....1..0....3..1....3..2....3..2....2..1....0..2....0..3....0..1....1..3

Links

Crossrefs

Cf. A265170, A046741.

Formula

a(n) = Sum_{k=0..n} (-1)^k*(2*n-2*k-1)!! * A046741(n,k) where and 0!! = (-1)!! = 1; proved by inclusion-exclusion, see [Young].

A265168 Number of n X 3 arrays containing 3 copies of 0..n-1 with no equal horizontal or vertical neighbors and new values introduced sequentially from 0.

Original entry on oeis.org

0, 1, 6, 447, 40476, 5693966, 1109065142, 286017249449, 94359717938545, 38773039478955950
Offset: 1

Views

Author

R. H. Hardin, Dec 03 2015

Keywords

Comments

Column 3 of A265170.

Examples

			Some solutions for n=4
..0..1..2....0..1..2....0..1..2....0..1..2....0..1..2....0..1..2....0..1..2
..1..3..0....3..0..3....2..3..0....1..3..0....2..3..1....1..2..1....1..2..3
..2..1..3....2..1..0....3..2..1....3..2..3....0..2..3....3..0..3....2..3..0
..3..0..2....1..3..2....1..3..0....2..0..1....3..1..0....2..3..0....3..0..1

Crossrefs

Cf. A265170.

A265169 Number of nX4 arrays of permutations of 4 copies of 0..n-1 with no equal horizontal or vertical neighbors and new values introduced sequentially from 0.

Original entry on oeis.org

0, 1, 19, 11223, 10723968, 19442592272, 58092310437590, 265923890299028745
Offset: 1

Views

Author

R. H. Hardin, Dec 03 2015

Keywords

Comments

Column 4 of A265170.

Examples

			Some solutions for n=4
..0..1..2..1....0..1..2..3....0..1..2..0....0..1..0..2....0..1..2..3
..3..2..1..0....2..3..1..0....3..2..1..3....1..3..1..3....1..2..3..0
..2..3..0..3....3..2..0..3....1..0..3..2....2..0..2..1....0..1..2..3
..3..0..1..2....1..0..1..2....0..2..1..3....3..2..3..0....2..3..1..0

Crossrefs

Cf. A265170.

A265171 Number of 5Xn arrays containing n copies of 0..5-1 with no equal horizontal or vertical neighbors and new values introduced sequentially from 0.

Original entry on oeis.org

1, 186, 40476, 10723968, 3152470670, 995141926013, 330443561580215, 113954535526102076, 40466434693734970267
Offset: 1

Views

Author

R. H. Hardin, Dec 03 2015

Keywords

Comments

Row 5 of A265170.

Examples

			Some solutions for n=3
..0..1..2....0..1..2....0..1..2....0..1..2....0..1..2....0..1..2....0..1..2
..1..0..3....3..4..0....2..3..4....3..2..4....3..2..0....3..4..0....3..4..0
..2..4..2....2..1..3....4..0..3....4..0..1....1..4..3....2..1..4....2..3..4
..4..3..4....4..3..4....1..3..4....3..2..3....0..2..4....1..0..3....1..2..3
..3..1..0....1..0..2....2..1..0....4..0..1....4..1..3....4..3..2....4..1..0

Crossrefs

Cf. A265170.
Showing 1-4 of 4 results.

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