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A171965
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Partial sums of floor(n^2/6) (A056827).
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2
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0, 0, 0, 1, 3, 7, 13, 21, 31, 44, 60, 80, 104, 132, 164, 201, 243, 291, 345, 405, 471, 544, 624, 712, 808, 912, 1024, 1145, 1275, 1415, 1565, 1725, 1895, 2076, 2268, 2472, 2688, 2916, 3156, 3409, 3675, 3955, 4249, 4557, 4879, 5216, 5568, 5936, 6320, 6720, 7136
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OFFSET
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0,5
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COMMENTS
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Quasipolynomial.
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} floor(k^2/6).
a(n) = round((2*n^3 + 3*n^2 - 12*n - 6)/36).
a(n) = round((4*n^3 + 6*n^2 - 24*n - 13)/72).
a(n) = floor((2*n^3 + 3*n^2 - 12*n + 7)/36).
a(n) = ceiling((2*n^3 + 3*n^2 - 12*n - 20)/36).
a(n) = a(n-6) + n^2 - 5*n + 7, n > 5.
G.f.: x^3*(1+x^2) / ( (1+x)*(1+x+x^2)*(x^2-x+1)*(x-1)^4 ). - R. J. Mathar, Jan 28 2012
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EXAMPLE
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a(5) = 7 = 0 + 0 + 0 + 1 + 2 + 4.
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MAPLE
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a(n):=round((2*n^3 +3*n^2 -12*n-6)/36)
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MATHEMATICA
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PROG
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(Magma) [Round((2*n^3+3*n^2-12*n-6)/36): n in [0..60]]; // Vincenzo Librandi, Jun 25 2011
(Python)
a171965 = [0]
for n in range(1, 60): a171965.append(a171965[-1] + n*n//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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