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 A056342 #37 Oct 13 2018 09:30:30
%S A056342 0,1,2,4,6,11,16,28,44,76,124,222,378,685,1222,2248,4110,7683,14308,
%T A056342 27010,50962,96907,184408,352696,675186,1296856,2493724,4806076,
%U A056342 9272778,17920858,34669600,67159048,130216122,252745366,490984486,954637556,1857545298,3617214679,7048675958,13744694926,26818405350
%N A056342 Number of bracelets of length n using exactly two different colored beads.
%C A056342 Turning over will not create a new bracelet.
%D A056342 M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]
%H A056342 G. C. Greubel, <a href="/A056342/b056342.txt">Table of n, a(n) for n = 1..3000</a>
%F A056342 a(n) = A000029(n) - 2.
%F A056342 From _Robert A. Russell_, Sep 26 2018: (Start)
%F A056342 a(n) = (A052823(n) + A027383(n-2)) / 2 = A059076(n) + A027383(n-2).
%F A056342 a(n) = (k!/4) * (S2(floor((n+1)/2),k) + S2(ceiling((n+1)/2),k)) + (k!/2n) * Sum_{d|n} phi(d) * S2(n/d,k), where k=2 is the number of colors and S2 is the Stirling subset number A008277.
%F A056342 G.f.: (k!/4) * x^(2k-2) * (1+x)^2 / Product_{i=1..k} (1-i x^2) - Sum_{d>0} (phi(d)/2d) * Sum_{j} (-1)^(k-j) * C(k,j) * log(1-j x^d), where k=2 is the number of colors. (End)
%e A056342 For a(6)=11, the arrangements are AAAAAB, AAAABB, AAABAB, AAABBB, AABAAB, AABBBB, ABABAB, ABABBB, ABBABB, ABBBBB, and AABABB, the last being chiral. Its reverse is AABBAB. - _Robert A. Russell_, Sep 26 2018
%t A056342 a[n_] := (1/4)*(Mod[n, 2] + 3)*2^Quotient[n, 2] + DivisorSum[n, EulerPhi[#]*2^(n/#)&]/(2*n) - 2; Array[a, 41] (* _Jean-François Alcover_, Nov 05 2017 *)
%t A056342 k=2; Table[k! DivisorSum[n, EulerPhi[#] StirlingS2[n/#,k]&]/(2n) + k!(StirlingS2[Floor[(n+1)/2], k] + StirlingS2[Ceiling[(n+1)/2], k])/4, {n,1,30}] (* _Robert A. Russell_, Sep 26 2018 *)
%o A056342 (PARI) a(n) = my(k=2); (k!/4)*(stirling(floor((n+1)/2),k,2) + stirling(ceil((n+1)/2),k,2)) + (k!/(2*n))*sumdiv(n,d,eulerphi(d)*stirling(n/d,k,2)); \\ _Michel Marcus_, Sep 28 2018
%Y A056342 Column 2 of A273891.
%Y A056342 Equals A052823 - A059076.
%Y A056342 Cf. A008277, A027383.
%K A056342 nonn
%O A056342 1,3
%A A056342 _Marks R. Nester_
%E A056342 More terms from _Joerg Arndt_, Jun 10 2016