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

Author

Hugo Pfoertner and Rainer Rosenthal, Feb 14 2021

Keywords

• nonn
• hard
• more

Examples

			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.
		

Links

• Stuart Anderson, Catalogues of Simple Perfect Squared Rectangles (SPSR).
• Stuart Anderson, Simple Imperfect Squared Rectangles, orders 9 to 24.

Crossrefs

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

Cf. A113881, A219158.

Programs

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.

Formula

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

Extensions

a(19) from Hugo Pfoertner, Mar 15 2021