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 1-10 of 11 results. Next

A195226 Number of lower triangles of an n X n 0..2 array with each element differing from all of its diagonal, vertical, antidiagonal and horizontal neighbors by one or less.

Original entry on oeis.org

3, 15, 155, 3151, 127785, 10322065, 1663418313, 535153390177, 343932423395227, 441776066934784687, 1134608168927438377475, 5828490619001307113164495, 59904949456032239303490933489, 1232191818850202836476827846621041
Offset: 1

Views

Author

R. H. Hardin Sep 13 2011

Keywords

Comments

Column 2 of A195232

Examples

			Some solutions for n=4
..2........1........1........1........2........2........0........2
..1.1......1.2......1.1......1.2......1.1......1.1......0.0......1.1
..0.1.1....1.1.2....1.1.1....1.2.2....1.1.0....0.1.1....1.0.1....0.0.0
..0.1.1.0..1.1.1.2..0.1.0.0..1.1.2.2..1.1.0.0..0.0.1.1..1.0.0.0..1.1.0.0

Links

A195227 Number of lower triangles of an n X n 0..3 array with each element differing from all of its diagonal, vertical, antidiagonal and horizontal neighbors by one or less.

Original entry on oeis.org

4, 22, 246, 5428, 237818, 20729610, 3601738548, 1249159521262, 865793424024974, 1200356073563114252, 3331551471246807302142, 18523112376180844925948966, 206425939461681776649215679048, 4613382950875473008207859661034814
Offset: 1

Views

Author

R. H. Hardin Sep 13 2011

Keywords

Comments

Column 3 of A195232

Examples

			Some solutions for n=4
..3........2........0........2........1........2........1........1
..3.2......3.2......1.1......1.2......1.0......2.3......1.0......0.1
..2.2.2....3.2.1....1.2.1....1.1.2....1.0.1....3.3.3....0.0.1....1.0.0
..3.2.3.3..2.2.2.1..2.2.2.1..1.2.1.1..1.0.1.2..3.3.2.3..1.0.1.0..1.0.0.1

Links

A195228 Number of lower triangles of an n X n 0..4 array with each element differing from all of its diagonal, vertical, antidiagonal and horizontal neighbors by one or less.

Original entry on oeis.org

5, 29, 337, 7705, 348849, 31374671, 5618308863, 2006626824777, 1431393426377379, 2041526404394580503, 5826929219460553056125, 33306813274969071019847237, 381509343842237775318179191165, 8761682347863104757428803661222769
Offset: 1

Views

Author

R. H. Hardin Sep 13 2011

Keywords

Comments

Column 4 of A195232

Examples

			Some solutions for n=4
..1........1........2........2........3........0........3........1
..2.1......2.1......1.2......1.1......3.2......0.0......4.4......1.2
..1.2.2....1.1.1....2.1.2....1.1.0....2.2.2....0.1.0....4.4.3....2.2.2
..1.1.2.3..1.0.1.2..1.2.1.2..1.0.1.1..2.2.3.2..0.1.1.1..4.4.4.3..1.1.2.2

Links

A195229 Number of lower triangles of an n X n 0..5 array with each element differing from all of its diagonal, vertical, antidiagonal and horizontal neighbors by one or less.

Original entry on oeis.org

6, 36, 428, 9982, 459880, 42029278, 7640055854, 2767861764930, 2001526172413328, 2892451174381411040, 8361331814456905846790, 48387254396810574882721328, 560941284568012233398098984786, 13033945031291662448750033149621602
Offset: 1

Views

Author

R. H. Hardin Sep 13 2011

Keywords

Comments

Column 5 of A195232

Examples

			Some solutions for n=4
..0........3........0........4........0........2........2........2
..1.1......4.4......1.0......4.4......1.1......1.1......1.2......3.2
..0.1.0....4.3.3....1.0.1....4.5.5....2.1.1....2.1.1....2.2.2....3.3.2
..1.0.1.0..4.4.3.3..1.1.1.2..4.4.5.5..2.1.1.1..2.1.1.2..3.3.2.1..2.3.2.2

Links

A195230 Number of lower triangles of an n X n 0..6 array with each element differing from all of its diagonal, vertical, antidiagonal and horizontal neighbors by one or less.

Original entry on oeis.org

7, 43, 519, 12259, 570911, 52683885, 9661943973, 3529267255201, 2571928557261907, 3744070741500225585, 10898903552323266521821, 63494356952926436300329797, 740796894931520786982829942993
Offset: 1

Views

Author

R. H. Hardin Sep 13 2011

Keywords

Comments

Column 6 of A195232

Examples

			Some solutions for n=4
..6........4........5........4........2........2........3........2
..5.5......4.4......4.5......4.4......2.3......2.2......4.4......1.2
..5.6.5....4.4.3....4.4.4....5.5.5....3.3.3....2.2.2....3.3.3....1.1.1
..6.6.5.4..4.3.3.4..3.4.4.3..5.6.5.6..2.2.2.3..1.2.1.1..3.4.4.3..1.0.1.1

Links

A195231 Number of lower triangles of an n X n 0..7 array with each element differing from all of its diagonal, vertical, antidiagonal and horizontal neighbors by one or less.

Original entry on oeis.org

8, 50, 610, 14536, 681942, 63338492, 11683832092, 4290676097374, 3142339851746238, 4595720660886942892, 13436641716584454488144, 78603060373509486868646762, 920680713893261032002755485080
Offset: 1

Views

Author

R. H. Hardin Sep 13 2011

Keywords

Comments

Column 7 of A195232

Examples

			Some solutions for n=4
..1........5........0........1........1........6........7........5
..0.1......6.5......1.0......2.2......2.1......5.6......7.6......5.4
..1.1.2....6.6.5....0.1.1....2.2.2....1.2.2....6.6.5....6.7.6....5.4.4
..0.1.1.2..6.6.6.6..1.0.1.2..2.1.2.2..1.1.1.2..6.6.6.6..6.6.6.7..5.4.4.3

Links

A195233 Number of lower triangles of a 3 X 3 0..n array with each element differing from all of its diagonal, vertical, antidiagonal and horizontal neighbors by one or less.

Original entry on oeis.org

64, 155, 246, 337, 428, 519, 610, 701, 792, 883, 974, 1065, 1156, 1247, 1338, 1429, 1520, 1611, 1702, 1793, 1884, 1975, 2066, 2157, 2248, 2339, 2430, 2521, 2612, 2703, 2794, 2885, 2976, 3067, 3158, 3249, 3340, 3431, 3522, 3613, 3704, 3795, 3886, 3977
Offset: 1

Views

Author

R. H. Hardin, Sep 13 2011

Keywords

Comments

Row 3 of A195232.

Examples

			Some solutions for n=4:
..2......1......0......2......1......3......2......0......4......3......0
..2.3....2.1....0.1....1.1....0.0....2.2....2.1....0.1....3.3....4.3....0.0
..2.3.3..1.1.2..0.1.1..2.2.1..0.0.0..2.2.1..2.1.1..1.0.0..3.4.4..3.3.4..0.1.1

Links

Crossrefs

Cf. A195232.

Formula

Empirical: a(n) = 91*n - 27.
Conjectures from Colin Barker, May 06 2018: (Start)
G.f.: x*(64 + 27*x) / (1 - x)^2.
a(n) = 2*a(n-1) - a(n-2) for n>2.
(End)

A195234 Number of lower triangles of a 4 X 4 0..n array with each element differing from all of its diagonal, vertical, antidiagonal and horizontal neighbors by one or less.

Original entry on oeis.org

1024, 3151, 5428, 7705, 9982, 12259, 14536, 16813, 19090, 21367, 23644, 25921, 28198, 30475, 32752, 35029, 37306, 39583, 41860, 44137, 46414, 48691, 50968, 53245, 55522, 57799, 60076, 62353, 64630, 66907, 69184, 71461, 73738, 76015, 78292, 80569
Offset: 1

Views

Author

R. H. Hardin, Sep 13 2011

Keywords

Comments

Row 4 of A195232.

Examples

			Some solutions for n=4:
..4........3........2........0........2........4........3........0
..3.3......2.2......2.3......1.1......1.1......3.4......2.3......1.1
..4.3.3....2.3.2....2.2.3....2.1.1....0.1.0....3.3.4....3.3.2....2.1.0
..3.3.2.3..3.3.2.3..1.2.2.3..1.2.2.2..1.0.0.1..4.4.3.4..2.2.3.3..1.1.1.0

Links

Crossrefs

Cf. A195232.

Formula

Empirical: a(n) = 2277*n - 1403 for n>1.
Conjectures from Colin Barker, May 06 2018: (Start)
G.f.: x*(1024 + 1103*x + 150*x^2) / (1 - x)^2.
a(n) = 2*a(n-1) - a(n-2) for n>3.
(End)

A195235 Number of lower triangles of a 5 X 5 0..n array with each element differing from all of its diagonal, vertical, antidiagonal and horizontal neighbors by one or less.

Original entry on oeis.org

32768, 127785, 237818, 348849, 459880, 570911, 681942, 792973, 904004, 1015035, 1126066, 1237097, 1348128, 1459159, 1570190, 1681221, 1792252, 1903283, 2014314, 2125345, 2236376, 2347407, 2458438, 2569469, 2680500, 2791531, 2902562, 3013593
Offset: 1

Views

Author

R. H. Hardin, Sep 13 2011

Keywords

Comments

Row 5 of A195232.

Examples

			Some solutions for n=4 with 0 and 4:
..0..........4..........4..........0..........4..........0..........0
..1.1........3.3........3.3........1.1........4.3........1.1........1.1
..2.2.2......2.2.2......2.2.2......1.2.2......3.3.2......2.2.2......2.2.2
..3.2.3.3....1.2.2.1....1.2.1.1....1.2.3.3....2.3.2.1....3.3.3.3....3.3.2.3
..2.3.2.3.4..1.2.2.1.0..2.1.1.0.1..2.2.3.3.4..3.2.2.1.0..2.3.4.4.4..4.3.3.3.4

Links

Crossrefs

Cf. A195232.

Formula

Empirical: a(n) = 111031*n - 95275 for n>2.
Conjectures from Colin Barker, May 06 2018: (Start)
G.f.: x*(32768 + 62249*x + 15016*x^2 + 998*x^3) / (1 - x)^2.
a(n) = 2*a(n-1) - a(n-2) for n>4.
(End)

A195236 Number of lower triangles of a 6 X 6 0..n array with each element differing from all of its diagonal, vertical, antidiagonal and horizontal neighbors by one or less.

Original entry on oeis.org

2097152, 10322065, 20729610, 31374671, 42029278, 52683885, 63338492, 73993099, 84647706, 95302313, 105956920, 116611527, 127266134, 137920741, 148575348, 159229955, 169884562, 180539169, 191193776, 201848383, 212502990, 223157597
Offset: 1

Views

Author

R. H. Hardin, Sep 13 2011

Keywords

Comments

Row 6 of A195232.

Examples

			Some solutions for n=5 with 0 and 5:
..5............5............5............0............5............0
..4.4..........4.4..........4.4..........0.1..........4.4..........1.1
..4.3.3........4.3.3........3.3.3........1.1.2........3.3.3........2.1.2
..3.3.3.2......4.3.3.2......3.2.2.2......1.2.2.3......2.2.2.2......1.1.2.3
..3.2.2.2.1....4.4.3.2.1....2.2.2.1.1....2.2.3.3.4....1.1.1.2.2....2.1.2.3.4
..2.2.1.2.1.0..4.3.3.2.1.0..3.2.2.1.0.0..2.3.2.3.4.5..0.1.1.2.1.2..1.2.2.3.4.5

Links

Crossrefs

Cf. A195232.

Formula

Empirical: a(n) = 10654607*n - 11243757 for n>3.
Conjectures from Colin Barker, May 06 2018: (Start)
G.f.: x*(2097152 + 6127761*x + 2182632*x^2 + 237516*x^3 + 9546*x^4) / (1 - x)^2.
a(n) = 2*a(n-1) - a(n-2) for n>5.
(End)
Showing 1-10 of 11 results. Next

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