A369591 a(n) = number of Yamanouchi words over the alphabet {1, 2, 3} of length n that start with 3.
0, 0, 1, 2, 5, 14, 35, 90, 245, 644, 1716, 4707, 12727, 34683, 96174, 264784, 732785, 2051338, 5719684, 16007081, 45160093, 127106181, 358743903, 1018566177, 2887666445, 8204375034
Offset: 1