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A229063
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Volume of the Johnson square pyramid (rounded down) with all the edge lengths equal to n.
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2
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0, 1, 6, 15, 29, 50, 80, 120, 171, 235, 313, 407, 517, 646, 795, 965, 1158, 1374, 1616, 1885, 2182, 2509, 2867, 3258, 3682, 4142, 4639, 5174, 5748, 6363, 7021, 7723, 8470, 9264, 10105, 10996, 11939, 12933, 13981, 15084, 16244, 17462, 18739, 20078, 21478, 22942
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OFFSET
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1,3
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COMMENTS
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Johnson square pyramid: Square base with four equilateral triangular-faces. All the edge lengths are equal to n.
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LINKS
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FORMULA
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a(n) = floor(n^3*sqrt(2)/6)
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EXAMPLE
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a(9)=171: Volume= sqrt(2)/6*n^3= sqrt(2)/6*9^3= 171.8269478 and floor(171.8269478)= 171.
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MAPLE
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floor(n^3*sqrt(2)/6) ;
end proc:
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MATHEMATICA
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Table[Floor[k^3*Sqrt[2]/6], {k, 1, 100}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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