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A292346
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The forgotten topological index of the Aztec diamond AZ(n) (see the Ramanes et al. reference, Theorem 2.1).
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0
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204, 748, 1548, 2604, 3916, 5484, 7308, 9388, 11724, 14316, 17164, 20268, 23628, 27244, 31116, 35244, 39628, 44268, 49164, 54316, 59724, 65388, 71308, 77484, 83916, 90604, 97548, 104748, 112204, 119916, 127884, 136108, 144588, 153324, 162316, 171564
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OFFSET
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1,1
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COMMENTS
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The forgotten topological index of a simple connected graph is the sum of the cubes of its vertex degrees.
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REFERENCES
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M. Imran and S. Hayat, On computation of topological indices of Aztec diamonds, Sci. Int. (Lahore), 26 (4), 1407-1412, 2014.
H. S. Ramanes and R. B. Jummannaver, Computation of Zagreb indices and forgotten index of Aztec diamond, Aryabhatta J. Math. and Informatics, Vol. 09, No. 01, 619-627, 2017.
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LINKS
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FORMULA
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a(n) = 128*n^2 + 160*n - 84.
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EXAMPLE
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a(1) = 204; indeed, the Aztec diamond AZ(1) has four vertices of degree 2, four vertices of degree 3, and one vertex of degree 4 (see p. 620 of the Ramanes et al. reference); consequently, a(1) = 4*8 + 4*27 + 1*64 = 32 + 108 + 64 = 204.
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MAPLE
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a := proc (n) options operator, arrow: 128*n^2+160*n-84 end proc: seq(a(n), n = 1 .. 40);
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MATHEMATICA
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CoefficientList[Series[4 (51 + 34 x - 21 x^2) / (1-x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Sep 24 2017 *)
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PROG
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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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