

A051389


Rational resistances requiring at least n 1ohm resistors in series or parallel.


3



1, 2, 4, 8, 20, 42, 102, 250, 610, 1486, 3710, 9228, 23050, 57718, 145288, 365820, 922194, 2327914, 5885800, 14890796, 37701452, 95550472, 242325118, 614869792, 1561228066
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OFFSET

1,2


COMMENTS

If x and y require xn and yn resistors respectively, then (x+y) and 1/(1/x + 1/y) require no more than (xn+yn). Inspired by a sci.math posting by Miguel A. Lerma (lerma(AT)math.nwu.edu).


LINKS

Table of n, a(n) for n=1..25.


EXAMPLE

a(5)=card({5,1/5,5/4,4/5,7/3,3/7,7/4,4/7,7/2,2/7,7/5,5/7,8/3,3/8,8/5,5/8, 5/6,7/6,6/5,7/6}). E.g. 6/5 is made from two resistors in series in parallel with three resistors in series, since 6/5 = 1/(1/2 + 1/3).


CROSSREFS

Cf. A048211, A046825.
Let T(x, n) = 1 if x can be constructed with n 1ohm resistors in a circuit, 0 otherwise. Then A048211 is t(n) = sum(T(x, n)) for all x (x is necessarily rational). Let H(x, n) = 1 if T(x, n) = 1 and T(x, k) = 0 for all k < n, 0 otherwise. Then A051389 is h(n) = sum(H(x, n)) for all x (x is necessarily rational).
Sequence in context: A272122 A323019 A105319 * A078006 A288476 A056952
Adjacent sequences: A051386 A051387 A051388 * A051390 A051391 A051392


KEYWORD

nonn,nice


AUTHOR

Hugo van der Sanden


EXTENSIONS

a(15)a(21) from Jon E. Schoenfield, Aug 28 2006
Definition corrected by Jon E. Schoenfield, Aug 27 2006
a(22)a(23) from Graeme McRae, Aug 18 2007
a(24)a(25) from Antoine Mathys, Mar 20 2017


STATUS

approved



