cp's OEIS Frontend

A381216 Number of isomers of C_n H_{2n+2} O_2.

%I A381216 #10 Feb 18 2025 19:40:35
%S A381216 1,2,5,11,28,69,179,463,1225,3246,8697,23366,63137,171051,465002,
%T A381216 1266831,3459262,9462393,25926939,71139400,195451500,537608802,
%U A381216 1480316960,4079977874,11254956840,31072771980,85850016944,237356027117,656657132953,1817758531055,5034725293449
%N A381216 Number of isomers of C_n H_{2n+2} O_2.
%H A381216 Andrew Howroyd, <a href="/A381216/b381216.txt">Table of n, a(n) for n = 0..1000</a>
%e A381216 a(2)=5 because the following compounds are possible:
%e A381216      | |       |   |       | |       |     |       |
%e A381216 -O-O-C-C-   -O-C-O-C-   -O-C-C-O-   -C-O-O-C-   -O-C-O-
%e A381216      | |       |   |       | |       |     |       |
%e A381216                                                   -C-
%e A381216                                                    |
%o A381216 (PARI) \\ here R(n) gives g.f. of A000598.
%o A381216 R(n)={my(g=O(x)); for(n=0, n, g = 1 + x*(g^3/6 + subst(g, x, x^2)*g/2 + subst(g, x, x^3)/3) + O(x*x^n)); g}
%o A381216 seq(n)={my(A=O(x*x^n), p=R(n), p2=subst(p,x,x^2) + A, q=(p^2+p2)/2, q2=subst(q,x,x^2) + A); Vec((p^2/(1 - x^2*q^2) + p2/(1 - x^2*q2))*(1 + x*q)/2)} \\ _Andrew Howroyd_, Feb 17 2025
%Y A381216 Cf. A000598, A000599, A000600, A000602, A000635, A000636.
%K A381216 nonn
%O A381216 0,2
%A A381216 _Erich Friedman_, Feb 17 2025
%E A381216 a(10) onwards from _Andrew Howroyd_, Feb 17 2025