A355588 - OEIS

%I #8 Jul 22 2022 16:44:13

%S 1,1,1,1,1,1,1,1,1,1,1,1,5,5,5,5,5,5,5,5,35,35,35,35,35,35,35,35,35,

%T 35,35,7,35,7,35,35,7,35,35,35,35,35,55,385,385,385,55,55,385,11,55,

%U 385,385,385,385,55,5005,455,5005,5005,455,5005,5005,5005,5005,5005,5005,5005,5005,1001,143,1001

%N T(j,k) are the denominators v in the representation R = s/t + (2*sqrt(3)/Pi)*u/v of the resistance between two nodes separated by the distance (j,k) in an infinite triangular lattice of one-ohm resistors, where T(j,k), j >= 0, 0 <= k <= floor(j/2) is an irregular triangle read by rows.

%C See A355585 for more information.

%e The triangle begins:

%e    1;

%e    1;

%e    1,  1;

%e    1,  1;

%e    1,  1,  1;

%e    1,  1,  1;

%e    5,  5,  5,  5;

%e    5,  5,  5,  5;

%e   35, 35, 35, 35, 35;

%e   35, 35, 35, 35, 35;

%o (PARI) See A355587.

%Y A355587 are the corresponding numerators u.

%Y A355585 and A355586 are s and t.

%K nonn,tabf,frac

%O 0,13

%A _Hugo Pfoertner_, Jul 09 2022