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A298612
The number of concave polygon classes.
1
0, 1, 3, 8, 14, 29, 53, 100, 180, 343, 623, 1172, 2182, 4105, 7701, 14590, 27584, 52475, 99867, 190732, 364710, 699237, 1342169, 2581412, 4971052, 9587563, 18512775, 35792550, 69273650, 134219777, 260301157, 505294108, 981706812
OFFSET
3,3
COMMENTS
A concave polygon has at least one concave interior corner angle, and at least three convex interior corner angles. Two concave polygon classes are equivalent if the cyclic ordering of the concave and convex interior angles of each are equal.
a(n) is also the number of combinatorial necklaces with n beads in 2 colors (black and white) with at least one white bead and no fewer than 3 black beads.
FORMULA
a(n) = A000031(n) - A004526(n) - 3, n >= 3.
a(n) = A262232(n)-1, n >= 3.
MATHEMATICA
Table[DivisorSum[n, EulerPhi[#] 2^(n/#) &]/n - Floor[n/2] - 3, {n, 3, 35}] (* Michael De Vlieger, Jan 28 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Stuart E Anderson, Jan 23 2018
STATUS
approved