cp's OEIS Frontend

A355567 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.

%I A355567 #8 Aug 01 2022 23:16:29
%S A355567 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 A355567 45,3465,15,105,21,315,7,693,231,45045,105,5,315,315,495,495,15015,
%U A355567 585,45045,7,315,45,3465,3465,45045,45045,15015,385,765765,315,35,3465,495,45045,6435,15015,45045,765765,9945,14549535
%N A355567 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 A355567 See A355565 for more information.
%C A355567 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 A355567 See A211074 for references and links.
%H A355567 Rainer Rosenthal, <a href="/A355567/b355567.txt">Table of n, a(n) for n = 0..135</a>, rows 0..15 of triangle, flattened.
%e A355567 The triangle begins:
%e A355567    1;
%e A355567    1,  1;
%e A355567    1,  1,  3;
%e A355567    1,  3,  3,  15;
%e A355567    3,  1, 15,   5, 105;
%e A355567    3, 15, 15,  35,  21, 315;
%e A355567   15,  1, 35, 105,  45,  45, 3465
%o A355567 (PARI) \\ uses function R(m, p, x) given in A355565
%o A355567 for (j=0, 8, for (k=0, j, my(q=(pi/2)*R(j, k)); print1(denominator(polcoef(q, 0, pi)), ", ")); print())
%Y A355567 A355566 are the corresponding numerators u.
%Y A355567 A355565 and A131406 (with changed offset) are s and t.
%Y A355567 Cf. A350670.
%K A355567 nonn,tabl,frac
%O A355567 0,6
%A A355567 _Hugo Pfoertner_, Jul 07 2022