login
A335412
a(n) is the number of edges formed by n-secting the angles of an equilateral triangle.
5
3, 12, 39, 54, 123, 144, 255, 282, 435, 432, 663, 702, 939, 984, 1263, 1314, 1635, 1692, 2055, 2082, 2523, 2592, 3039, 3114, 3603, 3684, 4215, 4302, 4875, 4932, 5583, 5682, 6339, 6444, 7143, 7254, 7995, 8112, 8895, 8982, 9843, 9972, 10839, 10974, 11883, 12024
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) + 240.
Conjectures from Colin Barker, Jun 08 2020: (Start)
G.f.: 3*x*(1 + 3*x + 8*x^2 + 2*x^3 + 14*x^4 + 2*x^5 + 14*x^6 + 2*x^7 + 14*x^8 - 10*x^9 + 25*x^10 + 11*x^11 - 6*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
CROSSREFS
Cf. A332376, A277402 (regions), A335411 (vertices), A335413 (ngons).
Sequence in context: A350787 A222643 A129014 * A332376 A341712 A261384
KEYWORD
nonn
AUTHOR
Lars Blomberg, Jun 08 2020
STATUS
approved