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 A374925 #7 Jul 25 2024 03:03:55
%S A374925 0,0,1,3,10,31,91,259,726,2007,5489,14888,40122,107574,287239,764405,
%T A374925 2028679,5371858,14198008,37467982,98749767,259984452,683865318,
%U A374925 1797500121,4721662597,12396308875,32531025970,85337831350,223794544179,586736215856,1537941527011
%N A374925 Number of n-color compositions of n having at least one pair of adjacent parts that are the same color.
%F A374925 G.f.: Sum_{i>0} ( x^(2*i)/((1 - x)*(1 - x + x^i)*(1 - Sum_{j>0} ((x^j)/(1 - x + x^j)))) )/( 1 - Sum_{k>0} ((x^k)/(1 - x)) ).
%F A374925 a(n) = A088305(n) - A242551(n).
%e A374925 a(4) = 10 counts: (1,1,1,1), (1,1,2_a), (1,1,2_b), (1,2_a,1), (1,3_a), (2_a,1,1), (2_a,2_a), (2_b,1,1), (2_b,2_b), (3_a,1).
%o A374925 (PARI)
%o A374925 C_x(N) = {my(x='x+O('x^N), h=(sum(i=1,N,(x^(2*i))/((1-x)*(1-x+x^i)*(1-sum(j=1,N, (x^j)/(1-x+x^j))))))/(1-sum(i=1,N,(x^i)/(1-x)))); concat([0,0],Vec(h))}
%o A374925 C_x(40)
%Y A374925 Cf. A003242, A088305, A242551, A330774, A374727, A374728.
%K A374925 nonn,easy
%O A374925 0,4
%A A374925 _John Tyler Rascoe_, Jul 24 2024