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A241223 Number of triangles on a centered hexagonal grid of size n. 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..200

Eric Weisstein's World of Mathematics, Hex Number.

Eric Weisstein's World of Mathematics, Triangle.

FORMULA

a(n) = A240826(n) - A241222(n).

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

EXAMPLE

For n = 2 the 32 triangles are the following:

/. *     * *     * .     . .     . .     . .     . *     * *

. * *   . * .   * * .   * * .   . * .   . * *   * . *   . . .

\. .     . .     . .     * .     * *     . *     . .     * .

-

/* .     . .     . *     * .     . *     * *     * .     . *

* . .   * . *   . . .   . . *   . . *   . . .   * . *   * . .

\. *     * .     * *     . *     * .     . *     . .     * .

-

/* .     . .     * *     * *     * .     . .     . .     . *

. . .   * . *   . . *   * . .   * . .   * . .   . . *   . . *

\* *     . *     . .     . .     * .     * *     * *     . *

-

/* .     . *     * .     . .     . .     . *     * .     . *

. * *   * * .   . * .   * * .   . * *   . * .   . . *   * . .

\. .     . .     * .     . *     * .     . *     * .     . *

CROSSREFS

Cf. A045996.

Sequence in context: A222606 A283854 A160314 * A283412 A227441 A067820

Adjacent sequences:  A241220 A241221 A241222 * A241224 A241225 A241226

KEYWORD

nonn

AUTHOR

Martin Renner, Apr 17 2014

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

STATUS

approved

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Last modified August 9 17:13 EDT 2022. Contains 356026 sequences. (Running on oeis4.)