A342568 1/a(n) is the current through the resistor at the central rung of an electrical ladder network made of 6*n+1 one-ohm resistors, fed by 1 volt at diametrically opposite ends of the ladder.

1, 7, 45, 239, 1157, 5307, 23497, 101467, 430089, 1796975, 7422437, 30373191, 123327373, 497484067, 1995542913, 7965875891, 31663779857, 125391332055, 494914083229, 1947613051807, 7643917792917, 29928228744587, 116921300015417, 455866012012299, 1774126607984665

Offset

0,2

Links

Table of n, a(n) for n=0..24.

Formula

a(n) = 8*a(n-1) - 18*a(n-2) + 8*a(n-3) - a(n-4); a(0)=1, a(1)=7, a(2)=45, a(3)=239.

G.f.: (3*x^3 - 7*x^2 + x - 1)/(x^2 - 4*x + 1)^2. - Joerg Arndt, Jun 11 2021

Example

   a(0)=1         a(1)=7                      a(2)=45
   o 1V       o-----o-----o 1V       o-----o-----o-----o-----o 1V
   |          |     |     |          |     |     |     |     |
   |          |     |     |          |     |     |     |     |
  1 A         |   1/7 A   |          |     |   1/45 A  |     |
   |          |     |     |          |     |     |     |     |
   |          |     |     |          |     |     |     |     |
   o 0V    0V o-----o-----o       0V o-----o-----o-----o-----o

Crossrefs

Bisection (odd indices) of A093652.

A001834(n)/a(n) is the total resistance of the network between diametrically opposite ends of the ladder.

Cf. A082630.

Sequence in context: A197369 A059937 A278682 * A323140 A236194 A230760

Adjacent sequences: A342565 A342566 A342567 * A342569 A342570 A342571

Keyword

nonn,easy

Author

Hugo Pfoertner, Jun 10 2021

Status

approved