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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.
7
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
KEYWORD
nonn,tabl,frac
AUTHOR
Hugo Pfoertner, Jul 07 2022
STATUS
approved