A391486 Number of nonequivalent essentially series series-parallel networks with longest path at most n edges and largest cut set of at most 2 edges.

1, 4, 12, 32, 75, 165, 340, 674, 1289, 2403, 4375, 7825, 13759, 23859, 40837, 69111, 115718, 191925, 315461, 514274, 831880, 1335960, 2130822, 3376877, 5318964, 8329795, 12973283, 20100004, 30986336, 47541630, 72609232, 110410262, 167186264, 252138220, 378781221

Offset

1,2

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Formula

G.f.: 1/((1 - x)^2*Product_{k>=1} (1 - x^k)^k) - 1/(1 - x) - x/(1 - x)^3.

a(n) = A037294(n) - A000217(n).

Prog

(PARI) seq(n) = Vec(1/((1 - x)^2*prod(k=1, n, (1 - x^k + O(x*x^n))^k)) - 1/(1 - x) - x/(1 - x)^3)

Crossrefs

Row 2 of A391485.

Cf. A000217, A037294.

Sequence in context: A233447 A127811 A361099 * A138517 A001934 A004403

Adjacent sequences: A391483 A391484 A391485 * A391487 A391488 A391489

Keyword

nonn

Author

Andrew Howroyd, Dec 17 2025

Status

approved