A110692 - OEIS

%I #12 Sep 06 2017 20:56:31

%S 1,29,275,1498,5846,18250,48546,114480,245751,489247,915629,1627418,

%T 2768740,4536884,7195828,11091888,16671645,24502305,35294647,49928714,

%U 69482402,95263102,128842550,172095040,227239155,296883171,384074289

%N 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 (see p. 243, M_n(LLAAAAL)).

%H G. C. Greubel, <a href="/A110692/b110692.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-1).

%F a(n) = (n+1)*(n+2)*(n+3)*(155*n^4 +911*n^3 +2062*n^2 +2122*n +840)/7!.

%F G.f.: (8*x^4+54*x^3+71*x^2+21*x+1)/(x-1)^8. - _Alois P. Heinz_, Feb 27 2015

%p a:=n->(n+1)*(n+2)*(n+3)*(155*n^4+911*n^3+2062*n^2+2122*n+840)/5040: seq(a(n),n=0..31);

%t CoefficientList[Series[(8*x^4 + 54*x^3 + 71*x^2 + 21*x + 1)/(x - 1)^8, {x, 0, 50}], x] (* _G. C. Greubel_, Sep 06 2017 *)

%o (PARI) x='x+O('x^50); Vec((8*x^4+54*x^3+71*x^2+21*x+1)/(x-1)^8) \\ _G. C. Greubel_, Sep 06 2017

%K nonn,easy

%O 0,2

%A _Emeric Deutsch_, Aug 03 2005