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a(n) = 2*(n^2 + 3*n + 1)^3.
1

%I #18 Jul 14 2024 16:14:52

%S 2,250,2662,13718,48778,137842,332750,715822,1409938,2590058,4496182,

%T 7447750,11859482,18258658,27303838,39805022,56745250,79303642,

%U 108879878,147120118,195944362,257575250,334568302,429843598,546718898

%N a(n) = 2*(n^2 + 3*n + 1)^3.

%C Kekulé numbers for certain benzenoids.

%D S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 310).

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).

%F G.f.: 2*(1 + 118*z + 477*z^2 + 132*z^3 - 13*z^4 + 6*z^5 - z^6)/(1-z)^7.

%p A109118:=n->2*(n^2+3*n+1)^3: seq(A109118(n), n=0..30);

%t Table[2 (n^2 + 3 n + 1)^3, {n, 0, 30}] (* _Wesley Ivan Hurt_, Feb 04 2017 *)

%Y Cf. A028387.

%K nonn,easy

%O 0,1

%A _Emeric Deutsch_, Jun 19 2005