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T(j,k) are the numerators u 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.
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%I #21 Aug 01 2022 23:16:11

%S 0,0,1,-2,2,4,-12,23,2,23,-184,40,-118,12,176,-940,3323,-1118,499,20,

%T 563,-24526,1234,-18412,13462,-626,118,6508,-130424,721937,-71230,

%U 327143,-1312,14369,262,88069,-4924064,191776,-6601046,2395676,-888568,131972,-300766,1624,91072

%N T(j,k) are the numerators u 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) = 0 and T(n,n) = A350669(n-1) for n > 0. - _Rainer Rosenthal_, Aug 01 2022

%D See A211074 for references and links.

%H Rainer Rosenthal, <a href="/A355566/b355566.txt">Table of n, a(n) for n = 0..135</a>, rows 0..15 of triangle, flattened.

%e The triangle begins:

%e 0;

%e 0, 1;

%e -2, 2, 4;

%e -12, 23, 2, 23;

%e -184, 40, -118, 12, 176;

%e -940, 3323, -1118, 499, 20, 563;

%e -24526, 1234, -18412, 13462, -626, 118, 6508;

%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(numerator(polcoef(q,0,pi)),", ")); print())

%Y A355567 are the corresponding denominators v.

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

%Y Cf. A350669.

%K tabl,frac,sign

%O 0,4

%A _Hugo Pfoertner_, Jul 07 2022