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A304163
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a(n) = 9*n^2 - 3*n + 1 with n>0.
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5
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7, 31, 73, 133, 211, 307, 421, 553, 703, 871, 1057, 1261, 1483, 1723, 1981, 2257, 2551, 2863, 3193, 3541, 3907, 4291, 4693, 5113, 5551, 6007, 6481, 6973, 7483, 8011, 8557, 9121, 9703, 10303, 10921, 11557, 12211, 12883, 13573, 14281
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OFFSET
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1,1
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COMMENTS
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a(n) provides the number of vertices in the HcDN1(n) network (see Fig. 3 in the Hayat et al. paper).
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LINKS
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FORMULA
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O.g.f.: x*(7 + 10*x + x^2)/(1 - x)^3.
E.g.f.: -1 + (1 + 3*x)^2*exp(x).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)
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EXAMPLE
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Illustration of the order 1 graph:
o---o
/ \ / \
o---o---o
\ / \ /
o---o
The order 2 graph is composed of 7 such hexagons and in general the HcDN1(n) graph is constructed from a honeycomb graph with each hexagon subdivided into triangles.
(End)
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MAPLE
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seq(9*n^2-3*n+1, n = 1 .. 40);
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PROG
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(PARI) Vec(x*(7 + 10*x + x^2)/(1 - x)^3 + O(x^40)) \\ Colin Barker, May 23 2018
(Julia) [9*n^2-3*n+1 for n in 1:40] |> println # Bruno Berselli, May 10 2018
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CROSSREFS
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First trisection of A002061 (without 1).
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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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