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A234729
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Volume of right regular hexagonal pyramid with height and side lengths n, rounded down.
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1
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0, 6, 23, 55, 108, 187, 297, 443, 631, 866, 1152, 1496, 1902, 2376, 2922, 3547, 4254, 5050, 5940, 6928, 8020, 9221, 10536, 11971, 13531, 15221, 17045, 19010, 21121, 23382, 25799, 28377, 31122, 34038, 37130, 40405, 43866, 47520, 51371, 55425, 59687
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n)= floor(n^2*evalf(sqrt(3)*3/2)*n/3) = floor(0.8660254040* n^3).
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EXAMPLE
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a(7) = 297: Volume = n^2 * evalf(sqrt(3)*3/2)* n/3 = 297.0467136 and floor(297.0467136) = 297.
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MAPLE
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KD:= proc() local a, b; a:=n^2*evalf(sqrt(3)*3/2)*n/3 ; b:=floor(a); RETURN(b): end: seq(KD(), n=1..100);
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MATHEMATICA
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Table[Floor[k^3*0.8660254040], {k, 1, 100}]
Table[Floor[(Sqrt[3] n^3)/2], {n, 100}] (* Harvey P. Dale, Apr 11 2020 *)
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PROG
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CROSSREFS
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Cf. A229063 (volume of square pyramid).
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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