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A335411 a(n) is the number of vertices formed by n-secting the angles of an equilateral triangle. 5
3, 7, 21, 25, 63, 67, 129, 133, 219, 199, 333, 337, 471, 475, 633, 637, 819, 823, 1029, 1009, 1263, 1267, 1521, 1525, 1803, 1807, 2109, 2113, 2439, 2419, 2793, 2797, 3171, 3175, 3573, 3577, 3999, 4003, 4449, 4429, 4923, 4927, 5421, 5425, 5943, 5947, 6489 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
See A277402 for illustrations.
LINKS
FORMULA
Empirically for 12 < n < 500: a(n) = a(n-2) + a(n-10) - a(n-12) + 120.
Conjectures from Colin Barker, Jun 08 2020: (Start)
G.f.: x*(3 + 4*x + 11*x^2 + 24*x^4 + 24*x^6 + 24*x^8 - 24*x^9 + 45*x^10 + 20*x^11 - 11*x^12) / ((1 - x)^3*(1 + x)^2*(1 - x + x^2 - x^3 + x^4)*(1 + x + x^2 + x^3 + x^4)).
a(n) = a(n-1) + a(n-2) - a(n-3) + a(n-10) - a(n-11) - a(n-12) + a(n-13) for n>13.
(End)
Colin Barker's recurrence conjecture holds for 13 < n <= 500. Lars Blomberg, Jun 12 2020
Empirical: a(2*k - 1) = 3*(4*k^2 - 6*k + 3), for k >= 1. - Ivan N. Ianakiev, Jul 15 2020
CROSSREFS
Cf. A331782, A277402 (regions), A335412 (edges), A335413 (ngons).
Sequence in context: A065496 A322922 A018479 * A331782 A090504 A018548
KEYWORD
nonn
AUTHOR
Lars Blomberg, Jun 08 2020
STATUS
approved

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Last modified March 29 10:44 EDT 2024. Contains 371268 sequences. (Running on oeis4.)