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A122047
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Degree of the polynomial P(n,x), defined by a Somos-6 type sequence: P(n,x)=(x^(n-1)*P(n-1,x)*P(n-5,x) + P(n-2,x)*P(n-4,x))/P(n-6,x), initialized with P(n,x)=1 at n<0.
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8
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0, 0, 1, 3, 6, 10, 15, 22, 31, 42, 55, 70, 88, 109, 133, 160, 190, 224, 262, 304, 350, 400, 455, 515, 580, 650, 725, 806, 893, 986, 1085, 1190, 1302, 1421, 1547, 1680, 1820, 1968, 2124, 2288, 2460, 2640, 2829, 3027
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OFFSET
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0,4
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COMMENTS
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Maximum Wiener index of all maximal 5-degenerate graphs with n vertices. (A maximal 5-degenerate graph can be constructed from a 5-clique by iteratively adding a new 5-leaf (vertex of degree 5) adjacent to 5 existing vertices.) The extremal graphs are 5th powers of paths, so the bound also applies to 5-trees. - Allan Bickle, Sep 15 2022
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LINKS
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FORMULA
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a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-5) - 3*a(n-6) + 3*a(n-7) - a(n-8);
o.g.f.: x^2/((x^4+x^3+x^2+x+1)(x-1)^4). (End)
a(n) = floor((n^3 + 6*n^2 + 5*n)/30). - Allan Bickle, Sep 15 2022
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MATHEMATICA
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p[n_] := p[n] = Cancel[Simplify[(x^(n - 1)p[n - 1]p[n - 5] + p[n - 2]*p[n - 4])/p[n - 6]]]; p[ -6] = 1; p[ -5] = 1; p[ -4] = 1; p[ -3] = 1; p[ -2] = 1; p[ -1] = 1; Table[Exponent[p[n], x], {n, 0, 20}]
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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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