cp's OEIS Frontend

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.

%I A342568 #12 Jun 12 2021 06:04:50
%S A342568 1,7,45,239,1157,5307,23497,101467,430089,1796975,7422437,30373191,
%T A342568 123327373,497484067,1995542913,7965875891,31663779857,125391332055,
%U A342568 494914083229,1947613051807,7643917792917,29928228744587,116921300015417,455866012012299,1774126607984665
%N 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.
%F A342568 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.
%F A342568 G.f.: (3*x^3 - 7*x^2 + x - 1)/(x^2 - 4*x + 1)^2. - _Joerg Arndt_, Jun 11 2021
%e A342568    a(0)=1         a(1)=7                      a(2)=45
%e A342568    o 1V       o-----o-----o 1V       o-----o-----o-----o-----o 1V
%e A342568    |          |     |     |          |     |     |     |     |
%e A342568    |          |     |     |          |     |     |     |     |
%e A342568   1 A         |   1/7 A   |          |     |   1/45 A  |     |
%e A342568    |          |     |     |          |     |     |     |     |
%e A342568    |          |     |     |          |     |     |     |     |
%e A342568    o 0V    0V o-----o-----o       0V o-----o-----o-----o-----o
%Y A342568 Bisection (odd indices) of A093652.
%Y A342568 A001834(n)/a(n) is the total resistance of the network between diametrically opposite ends of the ladder.
%Y A342568 Cf. A082630.
%K A342568 nonn,easy
%O A342568 0,2
%A A342568 _Hugo Pfoertner_, Jun 10 2021