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A174060
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a(n) = Sum_{k=0..n} floor(sqrt(k))^2.
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4
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0, 1, 2, 3, 7, 11, 15, 19, 23, 32, 41, 50, 59, 68, 77, 86, 102, 118, 134, 150, 166, 182, 198, 214, 230, 255, 280, 305, 330, 355, 380, 405, 430, 455, 480, 505, 541, 577, 613, 649, 685, 721, 757, 793, 829, 865, 901, 937, 973, 1022, 1071, 1120, 1169, 1218, 1267, 1316
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OFFSET
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0,3
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COMMENTS
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LINKS
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FORMULA
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a(n) = (1/6)*m*(6*m*n - (m+1)*(3*m^2+m-1)) with m = floor(sqrt(n)). - Yalcin Aktar, Jan 30 2012
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MATHEMATICA
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Accumulate[Table[Floor[Sqrt[k]]^2, {k, 0, 59}]] (* Harvey P. Dale, Jul 13 2013 *)
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PROG
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(Python)
from math import isqrt
(Python)
from math import isqrt
def A174060(n): return ((m:=isqrt(n+1))*(6*m*(n+1) - (m+1)*(3*m**2+m-1)))//6
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CROSSREFS
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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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