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A206809
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Sum_{0<j<k<=n} k^3-j^3.
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3
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7, 52, 208, 608, 1463, 3080, 5880, 10416, 17391, 27676, 42328, 62608, 89999, 126224, 173264, 233376, 309111, 403332, 519232, 660352, 830599, 1034264, 1276040, 1561040, 1894815, 2283372, 2733192, 3251248, 3845023, 4522528, 5292320
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OFFSET
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2,1
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COMMENTS
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Partial sums of A206808. For a guide to related sequences, see A206817.
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LINKS
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FORMULA
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a(n) = (n*(-4-15*n-5*n^2+15*n^3+9*n^4))/60. G.f.: x^2*(x^2+10*x+7) / (x-1)^6. - Colin Barker, Jul 11 2014
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EXAMPLE
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a(3) = (8-1) + (27-1) + (27-8) = 52.
a(4) = a(3) + (64-1) + (64-8) + (64-27) = 208.
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MATHEMATICA
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s[k_] := k^3; t[1] = 0;
p[n_] := Sum[s[k], {k, 1, n}];
c[n_] := n*s[n] - p[n];
t[n_] := t[n - 1] + (n - 1) s[n] - p[n - 1]
Table[c[n], {n, 2, 50}] (* A206808 *)
Flatten[Table[t[n], {n, 2, 35}]] (* A206809 *)
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PROG
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(PARI) vector(100, n, n*(9*n^4+60*n^3+145*n^2+150*n+56)/60) \\ Colin Barker, Jul 11 2014
(PARI) Vec(x^2*(x^2+10*x+7)/(x-1)^6 + O(x^100)) \\ Colin Barker, Jul 11 2014
(Sage) [sum([sum([k^3-j^3 for j in range(1, k)]) for k in range(2, n+1)]) for n in range(2, 33)] # Danny Rorabaugh, Apr 18 2015
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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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