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A173704
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Partial sums of floor(n^3/2).
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1
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0, 0, 4, 17, 49, 111, 219, 390, 646, 1010, 1510, 2175, 3039, 4137, 5509, 7196, 9244, 11700, 14616, 18045, 22045, 26675, 31999, 38082, 44994, 52806, 61594, 71435, 82411, 94605, 108105, 123000, 139384, 157352, 177004, 198441, 221769, 247095, 274531, 304190, 336190, 370650, 407694, 447447, 490039, 535601, 584269, 636180, 691476, 750300, 812800
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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) = Sum_{k=0..n} floor(k^3/2).
a(n) = round((n^4+2*n^3+n^2-2*n)/8).
a(n) = round((n^4+2*n^3+n^2-2*n-1)/8).
a(n) = floor((n^4+2*n^3+n^2-2*n)/8).
a(n) = ceiling((n-1)*(n+1)*(n^2+2*n+2)/8).
a(n) = a(n-2)+(n-1)*(2*n^2-n+2)/2, n>1.
a(n) = 4*a(n-1) - 5*a(n-2) + 5*a(n-4) - 4*a(n-5) + a(n-6).
G.f.: -x^2*(4+x+x^2) / ( (1+x)*(x-1)^5 ).
a(n) = (n^4 + 2*n^3 + n^2 - 2*n - 1 + (-1)^n)/8. (End)
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EXAMPLE
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a(4) = floor(1/2) + floor(8/2) + floor(27/2) + floor(64/2) = 49.
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MAPLE
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A173704 := proc(n) (n^4+2*n^3+n^2-2*n-1+(-1)^n)/8 ; end proc:
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MATHEMATICA
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Table[Sum[Floor[k^3/2], {k, 0, n}], {n, 0, 50}] (* G. C. Greubel, Nov 23 2016 *)
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PROG
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(Magma) [Round((n^4+2*n^3+n^2-2*n)/8): n in [0..40]]; // Vincenzo Librandi, Jun 22 2011
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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