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.

A215229 Number of length-6 0..k arrays connected end-around, with no sequence of L

Original entry on oeis.org

0, 18, 408, 2940, 12600, 40110, 105168, 240408, 496080, 945450, 1690920, 2870868, 4667208, 7313670, 11104800, 16405680, 23662368, 33413058, 46299960, 63081900, 84647640, 112029918, 146420208, 189184200, 241878000, 306265050, 384333768
Offset: 1

Views

Author

R. H. Hardin, Aug 06 2012

Keywords

Comments

Row 6 of A215228.

Examples

			Some solutions for n=5:
..2....1....5....4....3....0....4....5....1....4....2....5....3....1....1....5
..0....3....2....2....1....4....1....4....2....1....3....3....4....4....4....1
..5....4....3....3....2....1....2....2....3....3....1....5....5....1....0....4
..0....5....0....2....4....5....4....0....2....2....3....0....0....5....4....2
..4....1....1....0....0....4....5....4....0....5....4....2....1....2....3....3
..1....2....3....2....5....3....2....3....5....3....5....0....5....0....5....4

Links

Crossrefs

Cf. A215228.

Formula

Empirical: a(n) = n^6 - 6*n^4 + 5*n^3 + 5*n^2 - 5*n.
Conjectures from Colin Barker, Jul 23 2018: (Start)
G.f.: 6*x^2*(3 + 47*x + 77*x^2 - 7*x^3) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
(End)

A215230 Number of length-7 0..k arrays connected end-around, with no sequence of L

Original entry on oeis.org

0, 0, 840, 10080, 57960, 228480, 710640, 1874880, 4379760, 9313920, 18378360, 34114080, 60180120, 101687040, 165590880, 261152640, 400468320, 599074560, 876634920, 1257711840, 1772629320, 2458431360, 3359941200, 4530926400
Offset: 1

Views

Author

R. H. Hardin, Aug 06 2012

Keywords

Comments

Row 7 of A215228.

Examples

			Some solutions for n=5:
..1....5....1....0....1....0....4....0....0....4....3....1....3....0....3....1
..2....4....3....1....0....3....0....4....5....2....0....4....5....3....2....2
..5....2....1....3....4....2....3....2....4....5....3....1....0....4....3....4
..3....4....5....1....5....3....4....5....1....4....5....2....5....5....5....0
..0....5....2....4....4....4....0....0....0....3....0....0....3....0....1....5
..5....1....5....1....3....2....5....2....4....0....3....2....0....2....2....3
..3....3....4....3....4....1....0....3....5....5....1....3....1....5....4....5

Links

Crossrefs

Cf. A215228.

Formula

Empirical: a(n) = n^7 - 7*n^5 + 14*n^3 - 8*n = n*(n-1)*(n-2)*(n+2)*(n+1)*(n^2-2).
Conjectures from Colin Barker, Jul 23 2018: (Start)
G.f.: 840*x^3*(1 + 4*x + x^2) / (1 - x)^8.
a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.
(End)

A215223 Number of length-n 0..3 arrays connected end-around, with no sequence of L

Original entry on oeis.org

4, 12, 24, 72, 120, 408, 840, 2448, 5760, 15960, 39864, 108024, 275184, 728784, 1895760, 4998528, 13033560, 34250904, 89602632, 235157640, 615871032
Offset: 1

Views

Author

R. H. Hardin, Aug 06 2012

Keywords

Comments

Column 3 of A215228.

Examples

			Some solutions for n=8:
..0....1....2....2....0....3....2....1....0....1....1....0....1....0....0....3
..3....3....3....3....1....0....3....0....2....2....0....3....3....2....3....1
..1....0....1....2....2....2....0....3....1....0....2....1....1....1....2....0
..2....2....0....1....3....1....2....0....3....3....3....2....2....3....1....1
..0....3....3....2....0....2....1....1....0....1....2....0....0....1....3....3
..2....0....0....0....3....3....0....3....3....3....1....3....1....0....1....0
..1....3....1....2....1....2....3....0....1....0....0....0....0....3....0....3
..2....2....3....1....2....0....1....2....3....2....3....1....2....2....2....2

A215224 Number of length-n 0..4 arrays connected end-around, with no sequence of L

Original entry on oeis.org

5, 20, 60, 240, 720, 2940, 10080, 38640, 140400, 529440, 1956900, 7335840, 27285180, 101960040, 380209980, 1419732000
Offset: 1

Views

Author

R. H. Hardin, Aug 06 2012

Keywords

Comments

Column 4 of A215228.

Examples

			Some solutions for n=8:
..2....2....1....4....4....3....3....1....0....0....1....1....4....4....4....4
..3....4....4....0....0....1....4....3....4....1....4....3....0....2....2....1
..2....0....3....2....4....2....2....4....1....0....3....0....3....3....1....3
..0....4....1....3....3....0....1....3....3....3....1....4....2....2....4....0
..1....3....2....4....0....1....3....0....2....2....3....3....1....1....0....3
..2....0....3....3....1....3....2....2....4....0....0....0....4....0....2....1
..4....2....0....1....0....0....0....4....3....1....3....2....3....2....0....0
..0....1....3....2....2....2....1....2....2....3....2....4....2....0....3....2

A215225 Number of length-n 0..5 arrays connected end-around, with no sequence of L

Original entry on oeis.org

6, 30, 120, 600, 2520, 12600, 57960, 280560, 1330560, 6394680, 30548760, 146516040, 701454000, 3361690080, 16104243120
Offset: 1

Views

Author

R. H. Hardin, Aug 06 2012

Keywords

Comments

Column 5 of A215228.

Examples

			Some solutions for n=8:
..3....0....1....3....0....0....3....3....0....3....3....3....0....0....4....0
..2....2....5....4....1....4....4....2....4....1....2....4....3....2....0....2
..1....1....4....2....0....5....0....0....0....4....5....1....1....3....4....5
..2....0....3....1....3....1....3....5....1....0....4....5....0....2....3....2
..0....3....5....5....4....3....1....2....5....3....0....0....4....4....5....0
..5....4....0....3....0....4....5....4....4....1....3....1....5....3....0....5
..2....2....3....1....4....5....2....2....1....2....1....0....0....2....2....1
..5....4....4....0....3....1....1....0....5....5....5....5....4....5....1....5

Crossrefs

Cf. A215228.

A215226 Number of length-n 0..6 arrays connected end-around, with no sequence of L

Original entry on oeis.org

7, 42, 210, 1260, 6720, 40110, 228480, 1338120, 7761600, 45291120, 263674950, 1537291560
Offset: 1

Views

Author

R. H. Hardin, Aug 06 2012

Keywords

Comments

Column 6 of A215228.

Examples

			Some solutions for n=5:
..6....4....6....0....4....3....0....2....2....4....4....2....0....2....3....0
..3....3....4....2....5....0....1....4....5....3....3....6....4....3....6....3
..6....4....6....1....0....2....4....6....0....5....2....4....5....0....0....1
..4....5....5....5....3....5....5....0....5....0....3....5....6....6....6....4
..1....6....1....2....6....6....3....4....3....5....0....3....3....0....5....6

A215227 Number of length-n 0..7 arrays connected end-around, with no sequence of L

Original entry on oeis.org

8, 56, 336, 2352, 15120, 105168, 710640, 4883424, 33384960, 228945360, 1568401296, 10751253072, 73683206688, 505043014560
Offset: 1

Views

Author

R. H. Hardin, Aug 06 2012

Keywords

Comments

Column 7 of A215228.

Examples

			Some solutions for n=5:
..7....2....0....6....7....7....6....7....3....7....6....0....1....2....5....0
..6....4....5....5....0....5....7....3....1....1....1....1....0....5....6....4
..1....3....6....7....6....7....5....7....5....5....5....2....7....1....3....1
..5....5....2....3....0....1....6....0....0....3....1....6....5....4....5....6
..0....6....1....5....4....4....1....6....4....4....7....7....0....0....7....4
Showing 1-7 of 7 results.

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