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A231655 Triangle T(n, k) read by rows giving number of non-equivalent ways to choose k points in an equilateral triangle grid of side n. 4
1, 1, 1, 1, 1, 1, 1, 2, 4, 6, 4, 2, 1, 1, 3, 10, 25, 41, 48, 41, 25, 10, 3, 1, 1, 4, 22, 87, 244, 526, 870, 1110, 1110, 870, 526, 244, 87, 22, 4, 1, 1, 5, 41, 238, 1029, 3450, 9147, 19524, 34104, 49231, 59038, 59038, 49231, 34104, 19524, 9147, 3450, 1029, 238 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

Number of orbits under dihedral group D_6 of order 6. - N. J. A. Sloane, Sep 12 2019

LINKS

Heinrich Ludwig, Table of n, a(n) for n = 0..173

EXAMPLE

Triangle T(n, k) is irregularly shaped: 0 <= k <= n*(n+1)/2+1. The first row corresponds to n = 1, the first column corresponds to k = 0. Rows are palindromic.

  1,  1;

  1,  1,  1,  1;

  1,  2,  4,  6,  4,  2,  1;

  1,  3, 10, 25, 41, 48, 41, 25, 10,  3,  1;

  ...

There are T(3, 2) = 4 nonisomorphic choices of 2 points (X) in an equilateral triangle grid of side 3:

      X       .       .       X

     . .     X X     . .     X .

    . X .   . . .   X . X   . . .

CROSSREFS

Columns k=1..5 are A001399, A227327, A230723, A231653, A231654.

Cf. A054252, A283113, A289709, A326611.

Sequence in context: A163234 A072984 A317310 * A018841 A182043 A138125

Adjacent sequences:  A231652 A231653 A231654 * A231656 A231657 A231658

KEYWORD

nonn,tabf

AUTHOR

Heinrich Ludwig, Nov 14 2013

STATUS

approved

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Last modified July 8 03:25 EDT 2020. Contains 335503 sequences. (Running on oeis4.)