|
%I #21 Sep 08 2022 08:45:20
%S 1,19,142,664,2330,6726,16848,37884,78243,150865,274846,477412,796276,
%T 1282412,2003280,3046536,4524261,6577743,9382846,13156000,18160846,
%U 24715570,33200960,44069220,57853575,75178701,96772014,123475852
%N Kekulé numbers for certain benzenoids.
%H Vincenzo Librandi, <a href="/A110694/b110694.txt">Table of n, a(n) for n = 0..1000</a>
%H S. J. Cyvin and I. Gutman, <a href="https://doi.org/10.1007/978-3-662-00892-8">Kekulé structures in benzenoid hydrocarbons</a>, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (see p. 243, M_n(LLLAALL)).
%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)*(n+4)*(34*n^3 + 199*n^2 + 355*n + 210)/7!.
%F a(0)=1, a(1)=19, a(2)=142, a(3)=664, a(4)=2330, a(5)=6726, a(6)=16848, a(7)=37884, a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8). - _Harvey P. Dale_, Feb 16 2014
%F G.f.: (1 + 11*x + 18*x^2 + 4*x^3)/(1 - x)^8. - _G. C. Greubel_, Sep 06 2017
%p a:=n->(n+1)*(n+2)*(n+3)*(n+4)*(34*n^3+199*n^2+355*n+210)/5040: seq(a(n),n=0..31);
%t Table[(n+1)(n+2)(n+3)(n+4)(34n^3+199n^2+355n+210)/5040,{n,0,30}] (* or *) LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{1,19,142,664,2330,6726,16848,37884},30] (* _Harvey P. Dale_, Feb 16 2014 *)
%o (Magma) [(n+1)*(n+2)*(n+3)*(n+4)*(34*n^3+199*n^2+355*n+210)/5040: n in [0..30]]; // _Vincenzo Librandi_, Mar 28 2012
%o (PARI) x='x+O('x^50); Vec((1 + 11*x + 18*x^2 + 4*x^3)/(1 - x)^8) \\ _G. C. Greubel_, Sep 06 2017
%K nonn,easy
%O 0,2
%A _Emeric Deutsch_, Aug 03 2005
|
