A355567 - OEIS

%I #8 Aug 01 2022 23:16:29

%S 1,1,1,1,1,3,1,3,3,15,3,1,15,5,105,3,15,15,35,21,315,15,1,35,105,45,

%T 45,3465,15,105,21,315,7,693,231,45045,105,5,315,315,495,495,15015,

%U 585,45045,7,315,45,3465,3465,45045,45045,15015,385,765765,315,35,3465,495,45045,6435,15015,45045,765765,9945,14549535

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

%C See A355565 for more information.

%C On the diagonal we have T(0,0) = 1 and T(n,n) = A350670(n-1) for n > 0. - _Rainer Rosenthal_, Aug 01 2022

%D See A211074 for references and links.

%H Rainer Rosenthal, <a href="/A355567/b355567.txt">Table of n, a(n) for n = 0..135</a>, rows 0..15 of triangle, flattened.

%e The triangle begins:

%e    1;

%e    1,  1;

%e    1,  1,  3;

%e    1,  3,  3,  15;

%e    3,  1, 15,   5, 105;

%e    3, 15, 15,  35,  21, 315;

%e   15,  1, 35, 105,  45,  45, 3465

%o (PARI) \\ uses function R(m, p, x) given in A355565

%o for (j=0, 8, for (k=0, j, my(q=(pi/2)*R(j, k)); print1(denominator(polcoef(q, 0, pi)), ", ")); print())

%Y A355566 are the corresponding numerators u.

%Y A355565 and A131406 (with changed offset) are s and t.

%Y Cf. A350670.

%K nonn,tabl,frac

%O 0,6

%A _Hugo Pfoertner_, Jul 07 2022