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A304506
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a(n) = 2*(3*n+1)*(9*n+8).
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2
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16, 136, 364, 700, 1144, 1696, 2356, 3124, 4000, 4984, 6076, 7276, 8584, 10000, 11524, 13156, 14896, 16744, 18700, 20764, 22936, 25216, 27604, 30100, 32704, 35416, 38236, 41164, 44200, 47344, 50596, 53956, 57424, 61000, 64684, 68476, 72376, 76384, 80500, 84724, 89056
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OFFSET
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0,1
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COMMENTS
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a(n) is the second Zagreb index of the single-defect 4-gonal nanocone CNC(4,n) (see definition in the Doslic et al. reference, p. 27).
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 CNC(4,n) is M(CNC(4,n);x,y) = 4*x^2*y^2 + 8*n*x^2*y^3 + 2*n*(3*n+1)*x^3*y^3.
More generally, the M-polynomial of CNC(k,n) is M(CNC(k,n); x,y) = k*x^2*y^2 + 2*k*n*x^2*y^3 + k*n*(3*n + 1)*x^3*y^3/2.
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LINKS
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FORMULA
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G.f.: 4*(4 + 22*x + x^2) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>2.
(End)
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MAPLE
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seq((2*(9*n+8))*(3*n+1), n = 0 .. 40);
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MATHEMATICA
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Table[2(3n+1)(9n+8), {n, 0, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {16, 136, 364}, 50] (* Harvey P. Dale, Aug 15 2022 *)
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PROG
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(PARI) a(n) = 2*(3*n+1)*(9*n+8); \\ Altug Alkan, May 14 2018
(GAP) List([0..50], n->2*(3*n+1)*(9*n+8)); # Muniru A Asiru, May 14 2018
(PARI) Vec(4*(4 + 22*x + x^2) / (1 - x)^3 + O(x^40)) \\ Colin Barker, May 14 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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