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.

0, 0, 1, -2, 2, 4, -12, 23, 2, 23, -184, 40, -118, 12, 176, -940, 3323, -1118, 499, 20, 563, -24526, 1234, -18412, 13462, -626, 118, 6508, -130424, 721937, -71230, 327143, -1312, 14369, 262, 88069, -4924064, 191776, -6601046, 2395676, -888568, 131972, -300766, 1624, 91072

Offset

0,4

Comments

See A355565 for more information.

On the diagonal we have T(0,0) = 0 and T(n,n) = A350669(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:
       0;
       0,    1;
      -2,    2,      4;
     -12,   23,      2,    23;
    -184,   40,   -118,    12,  176;
    -940, 3323,  -1118,   499,   20, 563;
  -24526, 1234, -18412, 13462, -626, 118, 6508;

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

Crossrefs

A355567 are the corresponding denominators v.

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

Cf. A350669.

Sequence in context: A134720 A019225 A002840 * A298477 A253677 A182894

Adjacent sequences: A355563 A355564 A355565 * A355567 A355568 A355569

Keyword

tabl,frac,sign

Author

Hugo Pfoertner, Jul 07 2022

Status

approved