OFFSET
1,3
COMMENTS
This sequence counts the CDE-descendants of a single edge A-Z.
[C]onnect: different nodes {P,Q} != {A,Z} may form a new edge P-Q.
[D]issect: any edge P-Q may be dissected into P-M-Q with a new node M.
[E]xtend: any node P not in {A,Z} may form a new edge P-Q with a new node Q.
These basic operations were motivated by A338487, which seemed to count the CDE-descendants of K_4 with edge A-Z removed.
REFERENCES
Technology Review's Puzzle Corner, How many different resistances can be obtained by combining 10 one ohm resistors? Oct 3, 2003.
LINKS
Joel Karnofsky, Solution of problem from Technology Review's Puzzle Corner Oct 3, 2003, Feb 23, 2004.
EXAMPLE
The a(3) = 3 CDE-descendants of A-Z with 3 edges are
.
A A A
( ) / /
o o - o o - o
| / \
Z Z Z
.
DCC DD DE
.
PROG
(PARI) \\ See A339065 for G.
InvEulerT(v)={my(p=log(1+x*Ser(v))); dirdiv(vector(#v, n, polcoef(p, n)), vector(#v, n, 1/n))}
seq(n)={my(A=O(x*x^n), g=G(2*n, x+A, []), gr=G(2*n, x+A, [1])/g, u=InvEulerT(Vec(-1+G(2*n, x+A, [1, 1])/(g*gr^2))), t=InvEulerT(Vec(-1+G(2*n, x+A, [2])/(g*subst(gr, x, x^2)))), v=vector(n)); for(n=1, #v, v[n]=(u[n]+t[n]-if(n%2==0, u[n/2]-v[n/2]))/2); v} \\ Andrew Howroyd, Nov 20 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Rainer Rosenthal, Nov 18 2020
EXTENSIONS
a(7)-a(25) from Andrew Howroyd, Nov 20 2020
STATUS
approved