

A051389


Number of rational resistances requiring exactly n 1ohm resistors in series or parallel.


7



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).
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 a(n) is h(n) = sum(H(x, n)) for all x (x is necessarily rational).


LINKS

Table of n, a(n) for n=1..25.
Index to sequences related to resistances.


FORMULA

a(n) = A153588(n)  A153588(n1) for n > 1.  Hugo Pfoertner, Nov 04 2020


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, A153588, A180414.
Sequence in context: A272122 A323019 A105319 * A078006 A288476 A338197
Adjacent sequences: A051386 A051387 A051388 * A051390 A051391 A051392


KEYWORD

nonn,nice,more


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
Definition changed to say "exactly".  N. J. A. Sloane, Nov 07 2020


STATUS

approved



