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.

A190091 Number of rhombuses on a (n+1) X 3 grid.

Original entry on oeis.org

2, 6, 10, 15, 20, 26, 32, 39, 46, 54, 62, 71, 80, 90, 100, 111, 122, 134, 146, 159, 172, 186, 200, 215, 230, 246, 262, 279, 296, 314, 332, 351, 370, 390, 410, 431, 452, 474, 496, 519, 542, 566, 590, 615, 640, 666, 692, 719, 746, 774, 802, 831, 860, 890, 920, 951, 982
Offset: 1

Views

Author

R. H. Hardin, May 04 2011

Keywords

Comments

Column 2 of A190098.

Examples

			All solutions for n=3:
..0..1....2..0....0..1....1..1....1..1....1..0....0..0....0..0....2..1....1..0
..1..0....2..1....0..2....2..0....1..2....1..2....0..1....0..2....2..2....1..1
..2..1....3..1....1..2....3..1....2..2....3..2....1..1....2..2....3..2....2..1
..1..2....3..0....1..1....2..2....2..1....3..0....1..0....2..0....3..1....2..0

Links

Crossrefs

Cf. A190098.

Formula

Empirical: a(n) = 2*a(n-1) -2*a(n-3) +a(n-4).
Conjectures from Colin Barker, May 04 2018: (Start)
G.f.: x*(2 + 2*x - 2*x^2 - x^3) / ((1 - x)^3*(1 + x)).
a(n) = (n^2 + 12*n - 4) / 4 for n even.
a(n) = (n^2 + 12*n - 5) / 4 for n odd.
(End)

A190092 Number of rhombuses on a (n+1) X 4 grid.

Original entry on oeis.org

3, 10, 22, 36, 50, 66, 82, 100, 120, 142, 164, 188, 212, 238, 264, 292, 320, 350, 380, 412, 444, 478, 512, 548, 584, 622, 660, 700, 740, 782, 824, 868, 912, 958, 1004, 1052, 1100, 1150, 1200, 1252, 1304, 1358, 1412, 1468, 1524, 1582, 1640, 1700, 1760, 1822, 1884
Offset: 1

Views

Author

R. H. Hardin, May 04 2011

Keywords

Comments

Column 3 of A190098.

Examples

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

Links

Crossrefs

Cf. A190098.

Formula

Empirical: a(n) = 2*a(n-1) -2*a(n-3) +a(n-4) for n>11.
Conjectures from Colin Barker, May 04 2018: (Start)
G.f.: x*(3 + 4*x + 2*x^2 - 2*x^3 - 5*x^4 + 2*x^8 - 2*x^10) / ((1 - x)^3*(1 + x)).
a(n) = (n^2 + 24*n - 56) / 2 for n>7 and even.
a(n) = (n^2 + 24*n - 57) / 2 for n>7 and odd.
(End)

A190093 Number of rhombuses on an (n+1) X 5 grid.

Original entry on oeis.org

4, 15, 36, 66, 96, 130, 164, 204, 248, 296, 344, 396, 448, 504, 560, 620, 680, 744, 808, 876, 944, 1016, 1088, 1164, 1240, 1320, 1400, 1484, 1568, 1656, 1744, 1836, 1928, 2024, 2120, 2220, 2320, 2424, 2528, 2636, 2744, 2856, 2968, 3084, 3200, 3320, 3440
Offset: 1

Views

Author

R. H. Hardin, May 04 2011

Keywords

Comments

Column 4 of A190098.

Examples

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

Links

Crossrefs

Cf. A190098.

Formula

Empirical: a(n) = 2*a(n-1) -2*a(n-3) +a(n-4) for n>11.
Conjectures from Colin Barker, May 04 2018: (Start)
G.f.: x*(4 + 7*x + 6*x^2 + 2*x^3 - 10*x^4 - 5*x^5 + 2*x^7 + 4*x^8 - 2*x^9 - 4*x^10) / ((1 - x)^3*(1 + x)).
a(n) = n^2 + 28*n - 84 for n>7 and even.
a(n) = n^2 + 28*n - 85 for n>7 and odd.
(End)

A190094 Number of rhombuses on a (n+1) X 6 grid.

Original entry on oeis.org

5, 20, 50, 96, 151, 212, 273, 344, 421, 504, 587, 676, 765, 860, 959, 1064, 1169, 1280, 1391, 1508, 1625, 1748, 1871, 2000, 2131, 2268, 2405, 2548, 2691, 2840, 2989, 3144, 3299, 3460, 3621, 3788, 3955, 4128, 4301, 4480, 4659, 4844, 5029, 5220, 5411, 5608
Offset: 1

Views

Author

R. H. Hardin, May 04 2011

Keywords

Examples

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

Links

Crossrefs

Column 5 of A190098.

Formula

Empirical: a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n>27.

A190095 Number of rhombuses on a (n+1)X7 grid.

Original entry on oeis.org

6, 26, 66, 130, 212, 312, 412, 527, 650, 782, 914, 1059, 1204, 1358, 1520, 1691, 1862, 2044, 2226, 2417, 2608, 2808, 3008, 3217, 3430, 3652, 3874, 4105, 4336, 4576, 4816, 5065, 5314, 5572, 5830, 6097, 6364, 6640, 6916, 7201, 7486, 7780, 8074, 8377, 8680
Offset: 1

Views

Author

R. H. Hardin May 04 2011

Keywords

Comments

Column 6 of A190098

Examples

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

Links

Formula

Empirical: a(n) = 2*a(n-1) -2*a(n-3) +a(n-4) for n>27

A190096 Number of rhombuses on a (n+1)X8 grid.

Original entry on oeis.org

7, 32, 82, 164, 273, 412, 564, 736, 918, 1112, 1306, 1520, 1734, 1960, 2198, 2448, 2698, 2964, 3230, 3508, 3790, 4084, 4378, 4684, 4996, 5320, 5644, 5980, 6316, 6664, 7012, 7372, 7732, 8104, 8480, 8868, 9256, 9656, 10056, 10468, 10880, 11304, 11728, 12164
Offset: 1

Views

Author

R. H. Hardin May 04 2011

Keywords

Comments

Column 7 of A190098

Examples

			Some solutions for n=3
..1..3....0..2....0..5....0..3....1..3....0..3....0..5....0..1....0..4....2..4
..1..5....1..1....1..3....1..5....2..0....0..6....1..4....1..3....0..7....2..5
..3..5....2..2....3..2....3..4....3..3....3..6....2..5....3..2....3..7....3..5
..3..3....1..3....2..4....2..2....2..6....3..3....1..6....2..0....3..4....3..4

Links

Formula

Empirical: a(n) = 2*a(n-1) -2*a(n-3) +a(n-4) for n>51

A190097 Number of rhombuses on a (n+1)X9 grid.

Original entry on oeis.org

8, 39, 100, 204, 344, 527, 736, 984, 1244, 1520, 1796, 2104, 2412, 2736, 3076, 3438, 3800, 4184, 4568, 4968, 5376, 5800, 6224, 6668, 7120, 7588, 8056, 8540, 9024, 9524, 10024, 10542, 11060, 11594, 12136, 12694, 13252, 13826, 14400, 14990, 15580, 16186
Offset: 1

Views

Author

R. H. Hardin May 04 2011

Keywords

Comments

Column 8 of A190098

Examples

			Some solutions for n=3
..0..3....1..1....1..5....0..5....0..5....1..0....0..5....0..4....2..4....1..3
..0..5....1..2....2..2....0..7....1..7....1..1....1..4....1..2....2..5....1..5
..2..5....2..2....3..5....2..7....3..6....2..1....2..5....2..4....3..5....3..5
..2..3....2..1....2..8....2..5....2..4....2..0....1..6....1..6....3..4....3..3

Links

Formula

Empirical: a(n) = 2*a(n-1) -2*a(n-3) +a(n-4) for n>51
Showing 1-7 of 7 results.

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