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.

A189807 Number of right triangles on an (n+1) X 3 grid.

Original entry on oeis.org

14, 44, 94, 158, 238, 330, 434, 550, 678, 818, 970, 1134, 1310, 1498, 1698, 1910, 2134, 2370, 2618, 2878, 3150, 3434, 3730, 4038, 4358, 4690, 5034, 5390, 5758, 6138, 6530, 6934, 7350, 7778, 8218, 8670, 9134, 9610, 10098, 10598, 11110, 11634, 12170, 12718
Offset: 1

Views

Author

R. H. Hardin, Apr 28 2011

Keywords

Comments

Column 2 of A189814.

Examples

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

Links

Crossrefs

Cf. A189814.

Formula

Empirical: a(n) = 6*n^2 + 26*n - 42 for n>3.
Conjectures from Colin Barker, May 03 2018: (Start)
G.f.: 2*x*(7 + x + 2*x^2 - 3*x^3 + x^4 - 2*x^5) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>6.
(End)

A189808 Number of right triangles on a (n+1) X 4 grid.

Original entry on oeis.org

28, 94, 200, 342, 524, 732, 972, 1236, 1524, 1840, 2180, 2544, 2932, 3344, 3780, 4240, 4724, 5232, 5764, 6320, 6900, 7504, 8132, 8784, 9460, 10160, 10884, 11632, 12404, 13200, 14020, 14864, 15732, 16624, 17540, 18480, 19444, 20432, 21444, 22480, 23540
Offset: 1

Views

Author

R. H. Hardin, Apr 28 2011

Keywords

Comments

Column 3 of A189814.

Examples

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

Links

Crossrefs

Cf. A189814.

Formula

Empirical: a(n) = 12*n^2 + 88*n - 240 for n>8.
Conjectures from Colin Barker, May 03 2018: (Start)
G.f.: 2*x*(14 + 5*x + x^2 - 2*x^3 + 2*x^4 - 7*x^5 + 3*x^6 - 4*x^7 + 2*x^9 - 2*x^10) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>8.
(End)

A189809 Number of right triangles on an (n+1) X 5 grid.

Original entry on oeis.org

46, 158, 342, 596, 926, 1308, 1754, 2250, 2794, 3390, 4026, 4702, 5426, 6190, 6994, 7838, 8726, 9654, 10622, 11630, 12678, 13766, 14894, 16062, 17270, 18518, 19806, 21134, 22502, 23910, 25358, 26846, 28374, 29942, 31550, 33198, 34886, 36614, 38382
Offset: 1

Views

Author

R. H. Hardin, Apr 28 2011

Keywords

Comments

Column 4 of A189814.

Examples

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

Links

Crossrefs

Cf. A189814.

Formula

Empirical: a(n) = 20*n^2 + 228*n - 930 for n>15.
Conjectures from Colin Barker, May 03 2018: (Start)
G.f.: 2*x*(23 + 10*x + 3*x^2 - x^3 + 3*x^4 - 12*x^5 + 6*x^6 - 7*x^7 - x^8 + 2*x^9 - 6*x^10 + 4*x^12 - 4*x^13 + 2*x^16 - 2*x^17) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>11.
(End)

A189810 Number of right triangles on a (n+1)X6 grid.

Original entry on oeis.org

68, 238, 524, 926, 1444, 2060, 2784, 3596, 4492, 5470, 6516, 7630, 8820, 10070, 11380, 12758, 14204, 15710, 17276, 18902, 20596, 22350, 24164, 26038, 27972, 29970, 32028, 34146, 36324, 38562, 40860, 43218, 45636, 48114, 50652, 53250, 55908, 58626, 61404
Offset: 1

Views

Author

R. H. Hardin Apr 28 2011

Keywords

Comments

Column 5 of A189814

Examples

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

Links

Formula

Empirical: a(n) = 30*n^2 + 468*n - 2478 for n>24

A189811 Number of right triangles on a (n+1)X7 grid.

Original entry on oeis.org

94, 330, 732, 1308, 2060, 2960, 4032, 5250, 6604, 8082, 9684, 11388, 13220, 15144, 17156, 19268, 21484, 23784, 26176, 28656, 31236, 33900, 36648, 39480, 42404, 45420, 48520, 51704, 54972, 58324, 61768, 65296, 68908, 72604, 76384, 80248, 84200, 88236
Offset: 1

Views

Author

R. H. Hardin Apr 28 2011

Keywords

Comments

Column 6 of A189814

Examples

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

Links

Formula

Empirical: a(n) = 42*n^2 + 886*n - 6080 for n>35

A189812 Number of right triangles on a (n+1)X8 grid.

Original entry on oeis.org

124, 434, 972, 1754, 2784, 4032, 5520, 7224, 9128, 11218, 13500, 15938, 18568, 21328, 24216, 27248, 30432, 33728, 37152, 40696, 44376, 48176, 52096, 56128, 60288, 64572, 68968, 73476, 78104, 82844, 87712, 92692, 97784, 102988, 108304, 113740, 119296
Offset: 1

Views

Author

R. H. Hardin Apr 28 2011

Keywords

Comments

Column 7 of A189814

Examples

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

Links

Formula

Empirical: a(n) = 56*n^2 + 1480*n - 12216 for n>48

A189813 Number of right triangles on a (n+1)X9 grid.

Original entry on oeis.org

158, 550, 1236, 2250, 3596, 5250, 7224, 9496, 12044, 14860, 17948, 21266, 24852, 28634, 32604, 36780, 41168, 45716, 50440, 55324, 60384, 65612, 71000, 76532, 82240, 88116, 94136, 100300, 106624, 113100, 119744, 126532, 133472, 140560, 147792
Offset: 1

Views

Author

R. H. Hardin Apr 28 2011

Keywords

Comments

Column 8 of A189814

Examples

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

Links

Formula

Empirical: a(n) = 72*n^2 + 2344*n - 23112 for n>63
Showing 1-7 of 7 results.

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