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