A331782 Total number of vertices in graph formed by the straight line segments connecting the edges of an equilateral triangle with the n-1 points resulting from a subdivision of the sides into n equal pieces, counting coinciding intersection points only once.

3, 7, 21, 25, 63, 67, 129, 133, 219, 223, 333, 337, 471, 475, 621, 637, 819, 823, 1029, 1021, 1263, 1267, 1521, 1477, 1803, 1807, 2109, 2113, 2439, 2431, 2793, 2797, 3171, 3175, 3549, 3577, 3999, 4003, 4449, 4417, 4923, 4903, 5421, 5425, 5859, 5947, 6489, 6397, 7059, 7063, 7653, 7657, 8271, 8275, 8889

Offset

1,1

Comments

a(n) <= 3*(n^2-n+1), with equality iff n is odd and not a member of A332378. A331423 gives the difference between a(n) and the upper bound.

Links

N. J. A. Sloane, Table of n, a(n) for n = 1..1000

Formula

a(n) = A091908(n) + 3*n.

Crossrefs

Cf. A091908, A092098 (number of cells), A332376 (number of edges), A332378, A331423.

Sequence in context: A322922 A018479 A335411 * A090504 A018548 A323585

Adjacent sequences: A331779 A331780 A331781 * A331783 A331784 A331785

Keyword

nonn

Author

N. J. A. Sloane, Feb 13 2020

Status

approved