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 1-7 of 7 results.

A201533 Number of n X 2 0..2 arrays with rows and columns lexicographically nondecreasing and every element equal to at least one horizontal or vertical neighbor.

Original entry on oeis.org

3, 9, 25, 69, 175, 410, 899, 1859, 3649, 6840, 12311, 21378, 35964, 58819, 93800, 146222, 223292, 334639, 492954, 714755, 1021293, 1439616, 2003809, 2756429, 3750155, 5049674, 6733825, 8898024, 11656994, 15147825, 19533390, 25006144
Offset: 1

Views

Author

R. H. Hardin, Dec 02 2011

Keywords

Comments

Column 2 of A201539.

Examples

			Some solutions for n=10:
..0..2....0..2....0..1....0..0....0..1....0..2....0..0....0..0....0..1....0..1
..0..2....0..2....0..1....0..1....0..1....0..2....0..0....0..1....0..1....0..1
..0..2....0..2....1..1....1..1....0..1....2..0....0..0....0..1....0..1....0..1
..0..2....0..2....1..2....1..1....0..1....2..0....0..2....0..2....1..0....0..1
..0..2....0..2....1..2....1..2....1..0....2..0....1..2....0..2....1..0....1..0
..1..1....1..0....1..2....1..2....1..0....2..0....1..2....0..2....1..0....1..0
..1..1....1..0....1..2....2..1....1..0....2..2....2..2....0..2....1..1....2..2
..1..2....2..0....2..0....2..1....2..1....2..2....2..2....2..1....2..1....2..2
..1..2....2..0....2..0....2..2....2..1....2..2....2..2....2..1....2..2....2..2
..1..2....2..2....2..2....2..2....2..2....2..2....2..2....2..1....2..2....2..2

Links

Crossrefs

Cf. A201539.

Formula

Empirical: a(n) = (1/40320)*n^8 - (1/3360)*n^7 + (23/2880)*n^6 - (1/48)*n^5 + (247/5760)*n^4 + (231/160)*n^3 - (6777/1120)*n^2 + (3121/168)*n - 20 for n>3.
Conjectures from Colin Barker, May 23 2018: (Start)
G.f.: x*(3 - 18*x + 52*x^2 - 84*x^3 + 76*x^4 - 25*x^5 - 19*x^6 + 20*x^7 + x^8 - 9*x^9 + 5*x^10 - x^11) / (1 - x)^9.
a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>12.
(End)

A201534 Number of nX3 0..2 arrays with rows and columns lexicographically nondecreasing and every element equal to at least one horizontal or vertical neighbor.

Original entry on oeis.org

3, 25, 111, 633, 3354, 16393, 72811, 293831, 1087857, 3735546, 12012530, 36466979, 105202136, 289996482, 767360174, 1956720113, 4824093641, 11531663892, 26793101230, 60636948110, 133921364986, 289121431541, 611037886807
Offset: 1

Views

Author

R. H. Hardin Dec 02 2011

Keywords

Comments

Column 3 of A201539

Examples

			Some solutions for n=7
..0..0..2....0..0..1....0..0..0....0..0..2....0..0..0....0..0..0....1..1..1
..0..2..2....0..2..1....0..0..0....0..1..2....0..2..2....0..0..2....1..1..2
..1..1..0....0..2..1....0..2..2....0..1..2....1..1..2....1..1..2....1..2..2
..2..1..0....2..0..0....1..1..1....0..1..2....1..1..2....1..2..1....1..2..2
..2..2..1....2..0..0....1..1..1....0..2..2....2..1..1....1..2..1....2..1..1
..2..2..1....2..0..2....2..0..0....2..2..1....2..1..1....2..2..1....2..2..1
..2..2..1....2..2..2....2..0..0....2..2..1....2..2..1....2..2..1....2..2..1

Links

Formula

Empirical: a(n) is a polynomial of degree 26 for n>13

A201535 Number of nX4 0..2 arrays with rows and columns lexicographically nondecreasing and every element equal to at least one horizontal or vertical neighbor.

Original entry on oeis.org

6, 69, 633, 7799, 91425, 983981, 9526987, 82847704, 652848538, 4712696751, 31480011434, 196280028176, 1150650039753, 6380377582098, 33631853768986, 169225758487160, 815686475352515, 3777731764480697, 16854911299206527
Offset: 1

Views

Author

R. H. Hardin Dec 02 2011

Keywords

Comments

Column 4 of A201539

Examples

			Some solutions for n=5
..0..0..0..1....0..0..0..1....0..0..2..2....0..0..1..2....0..0..2..2
..0..0..2..1....0..0..0..1....0..2..2..2....1..1..1..2....0..1..0..0
..0..1..2..2....0..1..2..2....1..1..1..2....1..2..0..0....0..1..1..1
..1..1..1..0....2..1..2..0....1..2..0..0....2..2..2..2....2..0..0..2
..2..2..0..0....2..1..2..0....1..2..0..0....2..2..2..2....2..0..2..2

Links

Formula

Empirical: a(n) is a polynomial of degree 80 for n>43

A201536 Number of nX5 0..2 arrays with rows and columns lexicographically nondecreasing and every element equal to at least one horizontal or vertical neighbor.

Original entry on oeis.org

9, 175, 3354, 91425, 2446147, 61807736, 1408677515, 28646055184, 523398227137, 8686880778087, 132361720458239, 1868645862989467, 24631940812325029, 305098771555173655, 3569810381726216867, 39630824798203404663
Offset: 1

Views

Author

R. H. Hardin Dec 02 2011

Keywords

Comments

Column 5 of A201539

Examples

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

Links

A201537 Number of nX6 0..2 arrays with rows and columns lexicographically nondecreasing and every element equal to at least one horizontal or vertical neighbor.

Original entry on oeis.org

13, 410, 16393, 983981, 61807736, 3762507339, 208164634003, 10298954399450, 457194210355549, 18377434753379050, 675525914078702215, 22913890806174601101, 722808878339707158532, 21342091118575178714919
Offset: 1

Views

Author

R. H. Hardin Dec 02 2011

Keywords

Comments

Column 6 of A201539

Examples

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

Links

A201538 Number of nX7 0..2 arrays with rows and columns lexicographically nondecreasing and every element equal to at least one horizontal or vertical neighbor.

Original entry on oeis.org

18, 899, 72811, 9526987, 1408677515, 208164634003, 28456420346436, 3505159734744220, 387870239576486118, 38812326822498760643, 3543738686502556683539, 297838575975499416278867
Offset: 1

Views

Author

R. H. Hardin Dec 02 2011

Keywords

Comments

Column 7 of A201539

Examples

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

Links

A201532 Number of n X n 0..2 arrays with rows and columns lexicographically nondecreasing and every element equal to at least one horizontal or vertical neighbor.

Original entry on oeis.org

0, 9, 111, 7799, 2446147, 3762507339, 28456420346436
Offset: 1

Views

Author

R. H. Hardin Dec 02 2011

Keywords

Comments

Diagonal of A201539

Examples

			Some solutions for n=4
..0..0..0..1....0..1..1..1....0..0..0..0....0..0..2..2....0..0..0..2
..0..0..0..1....0..1..2..2....0..1..2..2....0..0..2..2....0..1..2..2
..0..0..0..1....0..1..2..2....0..1..2..2....1..1..2..2....2..1..1..1
..0..0..1..1....2..2..2..2....1..1..2..2....2..2..1..1....2..2..2..1
Showing 1-7 of 7 results.

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