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A304165
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a(n) = 324*n^2 - 336*n + 102 (n >= 1).
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2
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90, 726, 2010, 3942, 6522, 9750, 13626, 18150, 23322, 29142, 35610, 42726, 50490, 58902, 67962, 77670, 88026, 99030, 110682, 122982, 135930, 149526, 163770, 178662, 194202, 210390, 227226, 244710, 262842, 281622, 301050, 321126, 341850, 363222, 385242, 407910, 431226, 455190, 479802, 505062
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OFFSET
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1,1
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COMMENTS
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a(n) is the first Zagreb index of the HcDN1(n) network (see Fig. 3 in the Hayat et al. manuscript).
The first Zagreb index of a simple connected graph is the sum of the squared degrees of its vertices. Alternatively, it is the sum of the degree sums d(i) + d(j) over all edges ij of the graph.
The M-polynomial of HcDN1(n) is M(HcDN1(n);x,y) = 6x^3*y^3 + 12(n-1)x^3*y^5 + 6nx^3*y^6 + 18(n-1)x^5*y^6 + (27n^2 -57n +30)x^6*y^6. - Emeric Deutsch, May 11 2018
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LINKS
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FORMULA
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G.f.: 6*x*(15 + 76*x + 17*x^2)/(1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3. (End)
E.g.f.: 6*(exp(x)*(17 - 2*x + 54*x^2) - 17). - Stefano Spezia, Apr 15 2023
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MAPLE
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seq(324*n^2-336*n+102, n=1..40);
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MATHEMATICA
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Table[324n^2-336n+102, {n, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {90, 726, 2010}, 40] (* Harvey P. Dale, Apr 12 2020 *)
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PROG
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(PARI) a(n) = 324*n^2-336*n+102; \\ Altug Alkan, May 09 2018
(PARI) Vec(6*x*(15 + 76*x + 17*x^2) / (1 - x)^3 + O(x^60)) \\ Colin Barker, May 10 2018
(GAP) List([1..40], n->324*n^2-336*n+102); # Muniru A Asiru, May 10 2018
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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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