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.

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, 45, 3465, 15, 105, 21, 315, 7, 693, 231, 45045, 105, 5, 315, 315, 495, 495, 15015, 585, 45045, 7, 315, 45, 3465, 3465, 45045, 45045, 15015, 385, 765765, 315, 35, 3465, 495, 45045, 6435, 15015, 45045, 765765, 9945, 14549535

Offset: 0

Author

Hugo Pfoertner, Jul 07 2022

Keywords

• nonn
• tabl
• frac

Comments

See A355565 for more information.

On the diagonal we have T(0,0) = 1 and T(n,n) = A350670(n-1) for n > 0. - Rainer Rosenthal, Aug 01 2022

Examples

			The triangle begins:
   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,  45, 3465
		

References

• See A211074 for references and links.

Links

• Rainer Rosenthal, Table of n, a(n) for n = 0..135, rows 0..15 of triangle, flattened.

Crossrefs

A355566 are the corresponding numerators u.

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

Cf. A350670.

Programs

PARI

\\ uses function R(m, p, x) given in A355565
for (j=0, 8, for (k=0, j, my(q=(pi/2)*R(j, k)); print1(denominator(polcoef(q, 0, pi)), ", ")); print())