

A180414


Number of different resistances that can be obtained by combining n oneohm resistors.


33



1, 2, 4, 8, 16, 36, 80, 194, 506, 1400, 4039, 12044, 36406, 111324, 342447, 1064835, 3341434, 10583931, 33728050, 107931849, 346616201
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OFFSET

0,2


COMMENTS

In "addendum" J. Karnofsky stated the value a(15) = 1064833. In contrast to the terms up to and including a(14), which could all be confirmed, an independent calculation based on a list of 3connected simple graphs resulted in the corrected value a(15) = 1064835.  Hugo Pfoertner, Dec 06 2020
See A337517 for the number of different resistances that can be obtained by combining /exactly/ n oneohm resistors. The method used by Andrew Howroyd (see his program in the link section) uses 3connected graphs with one edge (the 'battery edge') removed.  Rainer Rosenthal, Feb 07 2021


REFERENCES

Technology Review's Puzzle Corner, How many different resistances can be obtained by combining 10 one ohm resistors? Oct 3, 2003.


LINKS

Andrew Howroyd, PARI program (includes scripts for other related sequences)


FORMULA

a(n) is the number of elements in the union of the sets SetA337517(k), k <= n, counted by A337517.  Rainer Rosenthal, Feb 07 2021


EXAMPLE

a(n) counts all resistances that can be obtained with fewer than n resistors as well as with exactly n resistors. Without a resistor the resistance is infinite, i.e., a(0) = 1. One 1ohm resistor adds resistance 1, so a(1) = 2. Two resistors in parallel give 1/2 ohm, while in series they give 2 ohms. So a(2) is the number of elements in the set {infinity, 1, 1/2, 2}, i.e., a(2) = 4.  Rainer Rosenthal, Feb 07 2021


MATHEMATICA

See link.


CROSSREFS



KEYWORD

nonn,nice,hard,more


AUTHOR



EXTENSIONS



STATUS

approved



