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A374296
a(n) is the integer part of the area of a regular n-gon whose side lengths are n.
1
3, 16, 43, 93, 178, 309, 500, 769, 1133, 1612, 2228, 3005, 3969, 5147, 6570, 8268, 10275, 12627, 15360, 18514, 22130, 26250, 30921, 36187, 42099, 48707, 56063, 64221, 73239, 83174, 94087, 106039, 119095, 133320, 148782, 165551, 183699, 203299
OFFSET
3,1
FORMULA
a(n) = floor(n^3/(4*tan(Pi/n))).
a(n) = n^4/(4*Pi) - (Pi/12)*n^2 + O(1). - Charles R Greathouse IV, Jul 03 2024
EXAMPLE
Areas of polygons (starting from n=3):
3.897... (equilateral triangle), so a(3) = 3,
16.000... (square), so a(4) = 16,
43.011... (pentagon), so a(5) = 43,
93.530... (hexagon), so a(6) = 93,
178.061... (heptagon), so a(7) = 178.
CROSSREFS
Cf. A064313.
Sequence in context: A271374 A147874 A092466 * A152618 A296947 A255211
KEYWORD
nonn
AUTHOR
Nicolay Avilov, Jul 03 2024
STATUS
approved