A060521 Number of 3 X n grids of black and white cells, no 3 of same color vertically or horizontally contiguous.

6, 36, 102, 378, 1260, 4374, 14946, 51384, 176238, 605022, 2076288, 7126302, 24457806, 83942100, 288096942, 988778082, 3393583068, 11647114446, 39974047290, 137194888728, 470866430838, 1616060190870, 5546478488640

Offset

1,1

Comments

The conjectured recursion is correct: For each n count the solutions separately where the last two rows differ in 0, 1, 2, or 3 places; a linear recursion is then readily found. The corresponding matrix has characteristic polynomial x^4 - 2 x^3 - 5 x^2 + 1, matching the recursion recursion a(n+4) = 2a(n+3) + 5a(n+2) - a(n). [From Hagen von Eitzen, Oct 21 2009]

Links

Table of n, a(n) for n=1..23.

Robert Dougherty-Bliss, Christoph Koutschan, Natalya Ter-Saakov, and Doron Zeilberger, The (Symbolic and Numeric) Computational Challenges of Counting 0-1 Balanced Matrices, arXiv:2410.07435 [math.CO], 2024. See p. 6.

Formula

Almost surely satisfies a(n+4) = 2a(n+3) + 5a(n+2) - a(n).

Crossrefs

Sequence in context: A207704 A207495 A207249 * A036141 A270205 A207443

Adjacent sequences: A060518 A060519 A060520 * A060522 A060523 A060524

Keyword

nonn

Author

Tom Womack (tom(AT)womack.net)

Extensions

More terms from Hagen von Eitzen, Oct 21 2009

Status

approved