|
| |
|
|
A036759
|
|
Number of mirror-symmetrical edge-rooted tree-like octagonal systems.
|
|
1
| |
|
|
1, 1, 3, 4, 15, 23, 94, 155, 661, 1139, 4983, 8844, 39362, 71360, 321561, 592361, 2694421, 5025849, 23029195, 43388208, 199990961, 379900479, 1759636142, 3365582261, 15652514944, 30112397278, 140531706444, 271707661708
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,3
|
|
|
REFERENCES
| J. Brunvoll et al., Enumeration of tree-like octagonal systems, J. Math. Chem., 21 (1997), 193-196.
S. J. Cyvin et al., Enumeration of tree-like octagonal systems: catapolyoctagons, ACH Models in Chem. 134 (1997), 55-70.
|
|
|
FORMULA
| G.f. V=V(x) satisfies x(x-2)V^3+2(x^2-3x+1)V^2+(-x^2-3x+2)V-x(x+2)=0.
|
|
|
MAPLE
| F := (2+3*V+6*V^2+2*V^3-(V+2)*sqrt(1+4*V+8*V^2+4*V^4))/2/(V^3+2*V^2-V-1): Order := 40: S := solve(series(F, V)=x, V);
|
|
|
PROG
| (PARI) a(n)=if(n<1, 0, polcoeff(serreverse((2*x^3+6*x^2+3*x+2-(x+2)*sqrt(4*x^4+8*x^2+4*x+1+x*O(x^n)))/2/(x^3+2*x^2-x-1)), n)) - Michael Somos Mar 10 2004
|
|
|
CROSSREFS
| Sequence in context: A095799 A109926 A065942 * A081405 A167367 A024858
Adjacent sequences: A036756 A036757 A036758 * A036760 A036761 A036762
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 28 2004
|
| |
|
|
