OFFSET
1,2
COMMENTS
a(n)/2^(5*n-3) is the probability that the top left and bottom right vertices of the 3 X n grid graph are still connected after each edge has been independently deleted with probability 1/2. - Pontus von Brömssen, May 25 2024
LINKS
Pontus von Brömssen, Table of n, a(n) for n = 1..728
Steven B Segletes, On the Electrical Connectivity of a 2-D, Randomly Distributed, Two-Component (Conducting/Insulating) Mixture, page 12 lists number for 3 X 3 maze.
Index entries for linear recurrences with constant coefficients, signature (54,-1077,10642,-57954,180960,-324992,325632,-165888,32768).
FORMULA
a(n) = 54*a(n-1) - 1077*a(n-2) + 10642*a(n-3) - 57954*a(n-4) + 180960*a(n-5) - 324992*a(n-6) + 325632*a(n-7) - 165888*a(n-8) + 32768*a(n-9) for n >= 10. - Pontus von Brömssen, May 25 2024
G.f.: (1 - 14*x + 52*x^2 + 90*x^3 - 960*x^4 + 2096*x^5 - 1792*x^6 + 512*x^7)/((1 - 15*x + 48*x^2 - 32*x^3)*(1 - 39*x + 444*x^2 - 2078*x^3 + 4224*x^4 - 3648*x^5 + 1024*x^6)). - Eugene Nonko, Nov 15 2024
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
Eugene Nonko, Nov 22 2021
EXTENSIONS
a(11)-a(18) from Martin Ehrenstein, Dec 13 2021
Name clarified by Eugene Nonko, Nov 18 2024
STATUS
approved