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

0,6

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

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.

Example

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

Prog

(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())

Crossrefs

A355566 are the corresponding numerators u.

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

Cf. A350670.

Sequence in context: A163270 A098743 A283484 * A130560 A088105 A030708

Adjacent sequences: A355564 A355565 A355566 * A355568 A355569 A355570

Keyword

nonn,tabl,frac

Author

Hugo Pfoertner, Jul 07 2022

Status

approved