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 1-6 of 6 results.

A241228 Number of isosceles triangles on a centered hexagonal grid of size n.

Original entry on oeis.org

0, 20, 252, 1296, 4232, 10668, 22956, 43832, 77160, 126972, 198176, 296976, 429252, 602876, 825552, 1106376, 1454192, 1879956, 2397024, 3014312, 3747564, 4609476
Offset: 1

Views

Author

Martin Renner, Apr 17 2014

Keywords

Comments

A centered hexagonal grid of size n is a grid with A003215(n-1) points forming a hexagonal lattice.

Links

Crossrefs

Cf. A186434.

Formula

a(n) = A241223(n) - A241227(n).

Extensions

a(7) from Martin Renner, May 31 2014
a(8)-a(22) from Giovanni Resta, May 31 2014

A241231 Number of triangles, distinct up to congruence, on a centered hexagonal grid of size n.

Original entry on oeis.org

0, 4, 34, 134, 379, 866, 1718, 3085, 5149, 8095, 12188, 17664, 24781, 33861, 45269, 59327, 76461, 97017, 121458, 150379, 184053, 223137, 268117, 319578, 378132, 444455, 519178, 602675, 696102, 800051, 914995, 1042094, 1181858, 1335414, 1503251, 1686811, 1886417, 2103007
Offset: 1

Views

Author

Martin Renner, Apr 17 2014

Keywords

Comments

A centered hexagonal grid of size n is a grid with A003215(n-1) points forming a hexagonal lattice.

Examples

			For n = 2 the four kinds of non-congruent triangles are the following:
/. *     * *     . *     * .
. * *   . . *   * . *   . . *
\. .     . .     . .     * .

Links

  • Eric Weisstein's World of Mathematics, Hex Number.
  • Eric Weisstein's World of Mathematics, Triangle.

Crossrefs

Cf. A028419, A241223.

Formula

a(n) = A241232(n) + A241233(n) + A241234(n) = A241236(n) + A241237(n).

Extensions

a(7) from Martin Renner, May 31 2014
a(8)-a(14) from Giovanni Resta, May 31 2014
More terms from Bert Dobbelaere, Oct 17 2022

A241224 Number of acute triangles on a centered hexagonal grid of size n.

Original entry on oeis.org

0, 8, 204, 1788, 8690, 30360, 85194, 205394, 441876, 870912, 1601708, 2783574, 4616220, 7358312, 11339430, 16972182, 24763604, 35328426, 49405944, 67873484, 91762128, 122276784
Offset: 1

Views

Author

Martin Renner, Apr 17 2014

Keywords

Comments

A centered hexagonal grid of size n is a grid with A003215(n-1) points forming a hexagonal lattice.

Examples

			For n = 2 the eight acute triangles are the following:
/. *     * *     * .     . .     . .     . .     * .     . *
. * *   . * .   * * .   * * .   . * .   . * *   . . *   * . .
\. .     . .     . .     * .     * *     . *     * .     . *

Links

Crossrefs

Cf. A190019, A241223.

Formula

a(n) = A241223(n) - A241225(n) - A241226(n).

Extensions

a(7) from Martin Renner, May 31 2014
a(8)-a(22) from Giovanni Resta, May 31 2014

A241225 Number of right triangles on a centered hexagonal grid of size n.

Original entry on oeis.org

0, 12, 216, 1104, 3708, 9396, 20304, 38868, 68364, 112632, 176076, 263832, 381924, 536424, 735240, 985896, 1296540, 1676508, 2137392, 2689248, 3344244, 4114020
Offset: 1

Views

Author

Martin Renner, Apr 17 2014

Keywords

Comments

A centered hexagonal grid of size n is a grid with A003215(n-1) points forming a hexagonal lattice.

Links

Crossrefs

Cf. A077435.

Formula

a(n) = A241223(n) - A241224(n) - A241226(n).

Extensions

a(7) from Martin Renner, May 31 2014
a(8)-a(22) from Giovanni Resta, May 31 2014

A241226 Number of obtuse triangles on a centered hexagonal grid of size n.

Original entry on oeis.org

0, 12, 480, 4488, 22278, 78288, 220374, 531594, 1143648, 2254440, 4145244, 7202190, 11940444, 19029300, 29318754, 43872402, 63999528, 91288794, 127642164, 175326336, 237000816, 315772032
Offset: 1

Views

Author

Martin Renner, Apr 17 2014

Keywords

Comments

A centered hexagonal grid of size n is a grid with A003215(n-1) points forming a hexagonal lattice.

Links

Crossrefs

Cf. A190020.

Formula

a(n) = A241223(n) - A241224(n) - A241225(n).

Extensions

a(7) from Martin Renner, May 31 2014
a(8)-a(22) from Giovanni Resta, May 31 2014

A241227 Number of scalene triangles on a centered hexagonal grid of size n.

Original entry on oeis.org

0, 12, 648, 6084, 30444, 107376, 302916, 732024, 1576728, 3111012, 5724852, 9952620, 16509336, 26321160, 40567872, 60724104, 88605480, 126413772, 176788476, 242874756, 328359624, 437553360
Offset: 1

Views

Author

Martin Renner, Apr 17 2014

Keywords

Comments

A centered hexagonal grid of size n is a grid with A003215(n-1) points forming a hexagonal lattice.

Links

Crossrefs

Cf. A190312.

Formula

a(n) = A241223(n) - A241228(n).

Extensions

a(7) from Martin Renner, May 31 2014
a(8)-a(22) from Giovanni Resta, May 31 2014
Showing 1-6 of 6 results.

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