A340920 a(n) is the number of distinct resistances that can be produced from a planar circuit with exactly n unit resistors.

1, 1, 2, 4, 9, 23, 57, 151, 427, 1263, 3807, 11549, 34843, 104459, 311317, 928719, 2776247, 8320757, 24967341, 74985337

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Stuart Anderson, Catalogues of Simple Perfect Squared Rectangles (SPSR).

Stuart Anderson, Simple Imperfect Squared Rectangles, orders 9 to 24.

Formula

a(n) = A337517(n) for n <= 9, a(n) < A337517(n) for n >= 10.

Example

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.

Prog

(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.

Crossrefs

Cf. A002840, A048211, A174283, A180414, A337516, A337517, A338511, A338601, A338602, A340921.

Cf. A113881, A219158.

Sequence in context: A135346 A174283 A337516 * A337517 A268172 A151404

Adjacent sequences: A340917 A340918 A340919 * A340921 A340922 A340923

Keyword

nonn,hard,more

Author

Hugo Pfoertner and Rainer Rosenthal, Feb 14 2021

Extensions

a(19) from Hugo Pfoertner, Mar 15 2021

Status

approved