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This paper is a new step in the project of systematic description of coloredknot polynomials started in arXiv:1506.00339. In this paper, we managed toexplicitly find the inclusive Racah matrix, i.e. the whole set of mixingmatrices in channels R^3->Q with all possible Q, for R=[3,1]. The calculationis made possible by the use of a newly-developed efficient highest-weightmethod, still it remains tedious. The result allows one to evaluate andinvestigate [3,1]-colored polynomials for arbitrary 3-strand knots, and thisconfirms many previous conjectures on various factorizations, universality, anddifferential expansions. We consider in some detail the next-to-twist-knotsthree-strand family (n,-1|1,-1) and deduce its colored HOMFLY. Also confirmedand clarified is the eigenvalue hypothesis for the Racah matrices, whichpromises to provide a shortcut to generic formulas for arbitraryrepresentations.

HOMFLY polynomials in representation [3,1] for 3-strand braids