A238822 Number of equilateral triangles bounded by the sides and diagonals of a regular 3n-gon.

1, 14, 69, 188, 465, 882, 1645, 2648, 4257, 6170, 9141, 12564, 17329, 22778, 30045, 38192, 48705, 60318, 74917, 90740, 110481, 131714, 157389, 184968, 217825, 252902, 294165, 337988, 388977, 442710, 505021, 570464, 645249, 723758, 812805, 906012, 1011025, 1120658, 1243437, 1371080

Offset: 1

Author

N. J. A. Sloane, Mar 07 2014

Keywords

• nonn
• nice

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..100
• Antreas Hatzipolakis and Giovanni Resta, Number of Equilateral Triangles in Regular 3n-gon, Postings to the Sequence Fans Mailing List, Apr 08 2013
• Andrew Howroyd, PARI Program, Sep 2024.
• Giovanni Resta, Illustration for a(3) = 69

Crossrefs

Cf. A006561.

Formula

Conjecture: For odd n, a(n) = n*(n+1)^3/2 - 3*n^2. - Vilim Lendvaj, Jul 24 2024

Extensions

a(6)-a(24) from Luca Petrone, Mar 28 2017

Corrected and extended by Vilim Lendvaj, Jul 24 2024

a(26) onwards from Andrew Howroyd, Sep 26 2024