cp's OEIS Frontend

A355566 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.

%I A355566 #21 Aug 01 2022 23:16:11
%S A355566 0,0,1,-2,2,4,-12,23,2,23,-184,40,-118,12,176,-940,3323,-1118,499,20,
%T A355566 563,-24526,1234,-18412,13462,-626,118,6508,-130424,721937,-71230,
%U A355566 327143,-1312,14369,262,88069,-4924064,191776,-6601046,2395676,-888568,131972,-300766,1624,91072
%N A355566 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 A355566 See A355565 for more information.
%C A355566 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 A355566 See A211074 for references and links.
%H A355566 Rainer Rosenthal, <a href="/A355566/b355566.txt">Table of n, a(n) for n = 0..135</a>, rows 0..15 of triangle, flattened.
%e A355566 The triangle begins:
%e A355566        0;
%e A355566        0,    1;
%e A355566       -2,    2,      4;
%e A355566      -12,   23,      2,    23;
%e A355566     -184,   40,   -118,    12,  176;
%e A355566     -940, 3323,  -1118,   499,   20, 563;
%e A355566   -24526, 1234, -18412, 13462, -626, 118, 6508;
%o A355566 (PARI) \\ uses function R(m, p, x) given in A355565
%o A355566 for (j=0, 8, for (k=0, j, my(q=(pi/2)*R(j,k)); print1(numerator(polcoef(q,0,pi)),", ")); print())
%Y A355566 A355567 are the corresponding denominators v.
%Y A355566 A355565 and A131406 (with changed offset) are s and t.
%Y A355566 Cf. A350669.
%K A355566 tabl,frac,sign
%O A355566 0,4
%A A355566 _Hugo Pfoertner_, Jul 07 2022