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 1-5 of 5 results.

A241223 Number of triangles on a centered hexagonal grid of size n.

Original entry on oeis.org

0, 32, 900, 7380, 34676, 118044, 325872, 775856, 1653888, 3237984, 5923028, 10249596, 16938588, 26924036, 41393424, 61830480, 90059672, 128293728, 179185500, 245889068, 332107188, 442162836, 581060024, 754545360, 969196896, 1232477192, 1552824900
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 32 triangles are the following:
/. *     * *     * .     . .     . .     . .     . *     * *
. * *   . * .   * * .   * * .   . * .   . * *   * . *   . . .
\. .     . .     . .     * .     * *     . *     . .     * .
-
/* .     . .     . *     * .     . *     * *     * .     . *
* . .   * . *   . . .   . . *   . . *   . . .   * . *   * . .
\. *     * .     * *     . *     * .     . *     . .     * .
-
/* .     . .     * *     * *     * .     . .     . .     . *
. . .   * . *   . . *   * . .   * . .   * . .   . . *   . . *
\* *     . *     . .     . .     * .     * *     * *     . *
-
/* .     . *     * .     . .     . .     . *     * .     . *
. * *   * * .   . * .   * * .   . * *   . * .   . . *   * . .
\. .     . .     * .     . *     * .     . *     * .     . *

Links

Crossrefs

Cf. A045996.

Formula

a(n) = A240826(n) - A241222(n).
a(n) = A241224(n) + A241225(n) + A241226(n) = A241227(n) + A241228(n).

Extensions

a(7) from Martin Renner, May 31 2014
a(8)-a(22) from Giovanni Resta, May 31 2014
Terms a(23) and beyond from Andrew Howroyd, Sep 18 2017

A241237 Number of isosceles triangles, distinct up to congruence, on a centered hexagonal grid of size n.

Original entry on oeis.org

0, 3, 15, 35, 69, 106, 162, 222, 300, 382, 486, 587, 715, 840, 997, 1147, 1313, 1491, 1700, 1890, 2129, 2341, 2598, 2842, 3126, 3394, 3711, 3995, 4341, 4641, 5024, 5349, 5750, 6128, 6540, 6959, 7381, 7772, 8255, 8722, 9252, 9688, 10220, 10698, 11277, 11806, 12381, 12905
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 three kinds of non-congruent isosceles triangles are the following:
/. *     * *     * .
. * *   . . *   . . *
\. .     . .     * .

Links

Crossrefs

Cf. A189978, A241228.

Formula

a(n) = A241231(n) - A241236(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

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

A241229 Number of acute isosceles triangles on a centered hexagonal grid of size n.

Original entry on oeis.org

0, 8, 144, 768, 2558, 6564, 14334, 27626, 48828, 80772, 126692, 190230, 275700, 388016, 532386, 714906, 941600, 1219410, 1556184, 1959608, 2438868, 3002700
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. A190317.

Formula

a(n) = A241228(n) - A241230(n).

Extensions

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

A241230 Number of obtuse isosceles triangles on a centered hexagonal grid of size n.

Original entry on oeis.org

0, 12, 108, 528, 1674, 4104, 8622, 16206, 28332, 46200, 71484, 106746, 153552, 214860, 293166, 391470, 512592, 660546, 840840, 1054704, 1308696, 1606776
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. A190318.

Formula

a(n) = A241228(n) - A241229(n).

Extensions

a(7) from Martin Renner, May 31 2014
a(8)-a(22) from Giovanni Resta, May 31 2014
Showing 1-5 of 5 results.

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