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

Author

Hugo Pfoertner, Jun 10 2021

Keywords

• nonn
• easy

Examples

			   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.

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