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

1, 2, 5, 11, 28, 69, 179, 463, 1225, 3246, 8697, 23366, 63137, 171051, 465002, 1266831, 3459262, 9462393, 25926939, 71139400, 195451500, 537608802, 1480316960, 4079977874, 11254956840, 31072771980, 85850016944, 237356027117, 656657132953, 1817758531055, 5034725293449

Offset: 0

Author

Erich Friedman, Feb 17 2025

Keywords

• nonn

Examples

			a(2)=5 because the following compounds are possible:
     | |       |   |       | |       |     |       |
-O-O-C-C-   -O-C-O-C-   -O-C-C-O-   -C-O-O-C-   -O-C-O-
     | |       |   |       | |       |     |       |
                                                  -C-
                                                   |
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000598, A000599, A000600, A000602, A000635, A000636.

Programs

PARI

\\ here R(n) gives g.f. of A000598.
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}
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

Extensions

a(10) onwards from Andrew Howroyd, Feb 17 2025