A334444 Number of unlabeled n-vertex graphs for which the lights out puzzle has a unique solution.

1, 1, 2, 4, 13, 47, 339, 4043, 98375, 4553432, 403286335

Offset

1,3

Links

Table of n, a(n) for n=1..11.

Bradley Forrest and Nicole Manno, Lights Out on a Random Graph, The PUMP Journal of Undergraduate Research, 5 (2022), 165-175; arXiv:2108.07349 [math.CO], 2021-2022. See Table 1.

Ian Short (ed.) and Andrei Zabolotskii (auth.), Problem 92.2, Irish Math. Soc. Bulletin, 92 (2023), p. 68; see also J. P. McCarthy (ed.) and the North Kildare Mathematics Problem Club (auth.), Solution 92.2, Irish Math. Soc. Bulletin, 94 (2024), p. 101. This essentially proves that A141040 is a bisection.

Eric Weisstein's World of Mathematics, Lights Out Puzzle

Crossrefs

Euler transform of A334443.

A141040 is a bisection.

Sequence in context: A005164 A246494 A362642 * A268951 A290722 A341378

Adjacent sequences: A334441 A334442 A334443 * A334445 A334446 A334447

Keyword

nonn,more

Author

Pontus von Brömssen, Apr 30 2020

Extensions

a(11) from Forrest and Manno added by Andrei Zabolotskii, Nov 24 2023

Status

approved