A075464 a(n) is the minimal number of nontrivial switch flippings needed to solve the all-ones lights out problem on an n X n square.

1, 4, 5, 4, 15, 28, 33, 40, 25, 44, 55, 72, 105, 56, 117, 104, 147, 188, 141, 224, 245, 276, 231, 270, 353, 356, 405, 416, 345, 376, 553, 428, 469, 520, 563, 600, 761, 772, 561, 696, 891, 940, 953, 772, 1069, 1188, 971, 1096, 1165, 1220, 1317, 1256, 1487, 1400

Offset: 1

Author

Eric W. Weisstein, Sep 17 2002

Keywords

• nonn
• nice

Comments

For squares having multiple possible solutions (see A075462, A075463), there may be nontrivial solutions involving *more* than this number of flips.

References

• See A075462 for references.

Links

• Zhao Hui Du, Table of n, a(n) for n = 1..78 (terms 1..60 from Max Alekseyev)
• Eric Weisstein's World of Mathematics, Lights Out Puzzle
• Zhao Hui Du, C code for the problem (please compile it using the latest gcc with option -O3 -msse4.2)

Crossrefs

Cf. A075462, A075463.

Extensions

a(26)-a(29) from Les Reid, Sep 09 2007

a(30)-a(38) from Max Alekseyev, Sep 17 2009

Extended by Max Alekseyev, Sep 20 2009