|
%I #12 Mar 15 2021 05:10:38
%S 1,1,2,4,9,23,57,151,427,1263,3807,11549,34843,104459,311317,928719,
%T 2776247,8320757,24967341,74985337
%N a(n) is the number of distinct resistances that can be produced from a planar circuit with exactly n unit resistors.
%H Stuart Anderson, <a href="http://www.squaring.net/sq/sr/spsr/spsr.html">Catalogues of Simple Perfect Squared Rectangles (SPSR)</a>.
%H Stuart Anderson, <a href="http://www.squaring.net/sq/sr/sisr/sisr.html">Simple Imperfect Squared Rectangles, orders 9 to 24</a>.
%F a(n) = A337517(n) for n <= 9, a(n) < A337517(n) for n >= 10.
%e a(10) = 3807, whereas A337517(10) = 3823. The difference of 16 resistances results from the 15 terms of A338601/A338602 and the resistance 34/27 not representable by a planar network of 10 resistors, whereas it (but not 27/34) can be represented by a nonplanar network of 10 resistors.
%o (PARI) Replace the list of 3-connected graphs corresponding to A338511 by the list of planar graphs provided in A002840 in _Andrew Howroyd_'s PARI program linked in A180414.
%Y Cf. A002840, A048211, A174283, A180414, A337516, A337517, A338511, A338601, A338602, A340921.
%Y Cf. A113881, A219158.
%K nonn,hard,more
%O 0,3
%A _Hugo Pfoertner_ and _Rainer Rosenthal_, Feb 14 2021
%E a(19) from _Hugo Pfoertner_, Mar 15 2021
|
