From the name "oddmodonacci", it seems pretty clear this sequence is related to the Fibonacci sequence.

I take "oddmod" to mean:

(1) a peculiar modification to the Fibonacci sequence, perhaps using the modulus operator, or

(2) a modification of the Fibonacci sequence related to odd (as opposed to even) numbers or elements (n=1,3,5,7,...), or

(3) a combination of (1) and (2).