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 1-3 of 3 results.

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

A241232 Number of acute triangles, distinct up to congruence, on a centered hexagonal grid of size n.

Original entry on oeis.org

0, 2, 14, 49, 134, 296, 580, 1034, 1720, 2691, 4043, 5841, 8193, 11178, 14935, 19567, 25197, 31954, 40006, 49521, 60596, 73442, 88238, 105158, 124432, 146220, 170802, 198278, 228999, 263185, 300988, 342775, 388775, 439269, 494462, 554839, 620474, 691717, 769060, 852639
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 two kinds of non-congruent acute triangles are the following:
/. *     * .
. * *   . . *
\. .     * .

Links

Crossrefs

Cf. A190021, A241224.

Formula

a(n) = A241231(n) - A241233(n) - A241234(n)

Extensions

a(7) from Martin Renner, May 31 2014
a(8)-a(18) from Giovanni Resta, May 31 2014
More terms from Bert Dobbelaere, Oct 17 2022

A241233 Number of right triangles, distinct up to congruence, on a centered hexagonal grid of size n.

Original entry on oeis.org

0, 1, 5, 13, 25, 42, 62, 86, 115, 150, 191, 234, 282, 334, 395, 455, 526, 601, 677, 762, 855, 947, 1045, 1152, 1261, 1378, 1498, 1619, 1757, 1900, 2041, 2176, 2334, 2507, 2661, 2838, 3011, 3174, 3379, 3577, 3773, 3967, 4179, 4389, 4618, 4848, 5090, 5311, 5559, 5792, 6068
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 only kind of non-congruent right triangles is the following:
/. *
* . *
\. .

Links

Crossrefs

Cf. A189979, A241225.

Formula

a(n) = A241231(n) - A241232(n) - A241234(n).

Extensions

a(7) from Martin Renner, May 31 2014
a(8)-a(21) from Giovanni Resta, May 31 2014
More terms from Bert Dobbelaere, Oct 17 2022
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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