  The tail of a sequence $\{P_n(q)\}_{n \in \mathbb{N}}$ of formal power series
in $\mathbb{Z}[[q]]$ is the formal power series whose first $n$ coefficients
agree up to a common sign with the first $n$ coefficients of $P_n$. This paper
studies the tail of a sequence of admissible trivalent graphs with edges
colored $n$ or $2n$. We use local skein relations to understand and compute the
tail of these graphs. We also give product formulas for the tail of such
trivalent graphs. Furthermore, we show that our skein theoretic techniques
naturally lead to a proof for the Andrews-Gordon identities for the two
variable Ramanujan theta function as well to corresponding identities for the
false theta function.
