A261204 Number of binary strings of length n that avoid the pattern x x^R x (x^R is the reversal of x).
1, 2, 4, 6, 10, 16, 24, 34, 50, 72, 100, 138, 188, 254, 342, 454, 598, 784, 1018, 1316, 1694, 2166, 2756, 3492, 4404, 5530, 6920, 8626, 10712, 13264, 16368, 20134, 24700, 30212, 36856, 44850, 54438, 65918, 79642, 96008, 115488, 138642, 166100, 198614, 237062
Offset: 0
Keywords
Examples
For n = 6, the substrings to be avoided are 000, 111, 011001, and 100110. There are 26 binary strings that avoid 000 and 111, so there are 26 - 2 = 24 binary strings of length 6 that avoid x x^R x.
Links
- Giovanni Resta, Table of n, a(n) for n = 0..100
- James D. Currie, Narad Rampersad, Binary words avoiding x x^R x and strongly unimodal sequences, arXiv:1508.02964 [math.CO], 2015.
- James D. Currie, Narad Rampersad, Binary words avoiding x x^R x and strongly unimodal sequences, Journal of Integer Sequences, Vol. 18 (2015), Article 15.10.3.
Extensions
a(25)-a(44) from Giovanni Resta, Aug 12 2015