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A175724
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Partial sums of floor(n^2/12).
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6
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0, 0, 0, 0, 1, 3, 6, 10, 15, 21, 29, 39, 51, 65, 81, 99, 120, 144, 171, 201, 234, 270, 310, 354, 402, 454, 510, 570, 635, 705, 780, 860, 945, 1035, 1131, 1233, 1341, 1455, 1575, 1701, 1834, 1974, 2121, 2275, 2436, 2604, 2780, 2964, 3156, 3356
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OFFSET
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0,6
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COMMENTS
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Maximum Wiener index of all maximal 6-degenerate graphs with n-2 vertices. (A maximal 6-degenerate graph can be constructed from a 6-clique by iteratively adding a new 6-leaf (vertex of degree 6) adjacent to 6 existing vertices.) The extremal graphs are 6th powers of paths, so the bound also applies to 6-trees. - Allan Bickle, Sep 18 2022
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LINKS
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FORMULA
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a(n) = round((2*n^3 + 3*n^2 - 18*n)/72).
a(n) = a(n-6) + (n-2)*(n-3)/2, n>5.
a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +a(n-6) -3*a(n-7) +3*a(n-8) -a(n-9), n>8.
G.f.: x^4/((x+1)*(x^2+x+1)*(x^2-x+1)*(x-1)^4).
An explicit formula appears in the Bickle/Che paper.
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MAPLE
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A175724 := proc(n) add( floor(i^2/12) , i=0..n) ; end proc:
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MATHEMATICA
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Accumulate[Floor[Range[0, 49]^2/12]]
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PROG
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(Magma) [ &+[ Floor(j^2/12): j in [0..n] ]: n in [0..60] ];
(PARI) vector(61, n, round((2*(n-1)^3 +3*(n-1)^2 -18*(n-1))/72) ) \\ G. C. Greubel, Dec 05 2019
(Sage) [round((2*n^3 +3*n^2 -18*n)/72) for n in (0..60)] # G. C. Greubel, Dec 05 2019
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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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