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A277983
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a(n) = 54*n^2 - 78*n + 36.
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0
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36, 12, 96, 288, 588, 996, 1512, 2136, 2868, 3708, 4656, 5712, 6876, 8148, 9528, 11016, 12612, 14316, 16128, 18048, 20076, 22212, 24456, 26808, 29268, 31836, 34512, 37296, 40188, 43188, 46296, 49512, 52836, 56268, 59808, 63456, 67212, 71076, 75048, 79128, 83316
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OFFSET
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0,1
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COMMENTS
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For n>=1, a(n) is the second Zagreb index of the triangular grid graph T[n] (see the West reference, p. 390). The second Zagreb index of a simple connected graph is the sum of the degree products d(i)d(j) over all edges ij of the graph.
The M-polynomial of the triangular grid graph T[n] is M(T[n], x, y) = 6*x^2*y^4 + 3*(n-1)*x^4*y^4 +6*(n-2)*x^4*y^6+3*(n-2)*(n-3)*x^6*y^6/2.
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REFERENCES
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D. B. West, Introduction to Graph Theory, 2nd edition, Prentice-Hall, 2001.
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LINKS
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FORMULA
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O.g.f.: 12*(14*x^2 - 8*x + 3)/(1 - x)^3.
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MAPLE
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seq(54*n^2-78*n+36, n=0..40);
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MATHEMATICA
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Table[54 n^2 - 78 n + 36, {n, 0, 50}] (* Bruno Berselli, Nov 11 2016 *)
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PROG
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(Sage) [54*n^2-78*n+36 for n in range(50)] # Bruno Berselli, Nov 11 2016
(Magma) [54*n^2-78*n+36: n in [0..50]]; // Bruno Berselli, Nov 11 2016
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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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