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%I #17 Oct 19 2023 07:37:18
%S 1,23,194,985,3668,11074,28728,66438,140415,276001,511082,900263,
%T 1519882,2473940,3901024,5982300,8950653,13101051,18802210,26509637,
%U 36780128,50287798,67841720,90405250,119117115,155314341,200557098
%N a(n) = (n+1)*(n+2)^2*(n+3)*(11*n^3 + 58*n^2 + 101*n + 60)/720.
%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. 230, no. 22).
%H Chai Wah Wu, <a href="/A108646/b108646.txt">Table of n, a(n) for n = 0..10000</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 From _Chai Wah Wu_, Jun 12 2016: (Start)
%F 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) for n > 7.
%F G.f.: (1 + 15*x + 38*x^2 + 21*x^3 + 2*x^4)/(1 - x)^8. (End)
%F E.g.f.: (1/6!)*(720 + 15840*x + 53640*x^2 + 56520*x^3 + 24030*x^4 + 4548*x^5 + 377*x^6 + 11*x^7)*exp(x). - _G. C. Greubel_, Oct 19 2023
%p a:=(n+1)*(n+2)^2*(n+3)*(11*n^3+58*n^2+101*n+60)/720: seq(a(n),n=0..30);
%t Table[(n+2)*(n+3)!*(11*n^3+58*n^2+101*n+60)/(6!*n!), {n,0,40}] (* _G. C. Greubel_, Oct 19 2023 *)
%o (Python)
%o A108646_list, m = [], [77, -85, 28, -1, 1, 1, 1, 1]
%o for _ in range(10001):
%o A108646_list.append(m[-1])
%o for i in range(7):
%o m[i+1] += m[i] # _Chai Wah Wu_, Jun 12 2016
%o (Magma) [(n+2)*(11*n^3+58*n^2+101*n+60)*Binomial(n+3,3)/120: n in [0..40]]; // _G. C. Greubel_, Oct 19 2023
%o (SageMath) [(n+2)*(11*n^3+58*n^2+101*n+60)*binomial(n+3,3)/120 for n in range(41)] # _G. C. Greubel_, Oct 19 2023
%Y Cf. A108645, A108647, A108648, A108649, A108650.
%K nonn,easy
%O 0,2
%A _Emeric Deutsch_, Jun 13 2005
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