This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A123350 #35 Sep 08 2022 08:45:28
%S A123350 1,3,14,46,117,251,478,834,1361,2107,3126,4478,6229,8451,11222,14626,
%T A123350 18753,23699,29566,36462,44501,53803,64494,76706,90577,106251,123878,
%U A123350 143614,165621,190067,217126,246978,279809,315811,355182,398126,444853
%N A123350 a(n) = (n^4 + 2n^3 + 5n^2 + 4)/4.
%C A123350 Kekulé numbers for certain benzenoids. - _Emeric Deutsch_, Oct 16 2006
%C A123350 Form the 2 X 3 matrix with first row C(n,0), C(n,1), and C(n,2) and second row C(n+1,0), C(n+1,1), and C(n+1,2), multiply it by its transpose to get a 2 X 2 matrix: its determinant = a(n). - _J. M. Bergot_, Sep 05 2013
%D A123350 S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (see p. 120).
%H A123350 G. C. Greubel, <a href="/A123350/b123350.txt">Table of n, a(n) for n = 0..1000</a>
%H A123350 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A123350 G.f.: (-1 + 2*x - 9*x^2 + 4*x^3 - 2*x^4) / (x-1)^5 . - _R. J. Mathar_, Oct 19 2012
%F A123350 a(n) = 1 + A117717(n+1). - _R. J. Mathar_, Sep 15 2013
%F A123350 E.g.f.: (x^4 + 8*x^3 + 18*x^2 + 8*x + 4)*exp(x)/4. - _G. C. Greubel_, Oct 12 2017
%p A123350 a:=n->(n^4+2*n^3+5*n^2+4)/4: seq(a(n),n=0..40); # _Emeric Deutsch_, Oct 16 2006
%t A123350 Table[(n^4 + 2*n^3 + 5*n^2 + 4)/4, {n,0,50}] (* _G. C. Greubel_, Oct 12 2017 *)
%o A123350 (PARI) for(n=0,50, print1((n^4 + 2*n^3 + 5*n^2 + 4)/4, ", ")) \\ _G. C. Greubel_, Oct 12 2017
%o A123350 (Magma) [(n^4 + 2*n^3 + 5*n^2 + 4)/4: n in [0..30]]; // _G. C. Greubel_, Oct 12 2017
%K A123350 nonn,easy
%O A123350 0,2
%A A123350 _N. J. A. Sloane_, Oct 10 2006
%E A123350 More terms from _Emeric Deutsch_, Oct 16 2006