Recurrence Proofs of  Identities in § 3 and § 6 of "Finite Rogers-Ramanujan Type Identities", Electronic J. Combin 10(1)(2003) #R13 presented as Maple V Release 4 worksheets. These worksheets have not been tested with later versions of Maple.

3.2-b
3.2-t
3.3-b
3.3-t
3.4
3.5-b
3.5-t
3.6
3.8: see [SS, Thm 3]
3.10
3.11-b
3.11-t
3.12: see [SS, Thm 1]
3.14-b: see [And1],
3.14-t : see [And5, p. 5., eqn. 1.12].
3.15
3.16
3.17: see Chapter 3.
3.18-b: see [And1]
3.18-t: see [And5, p. 5, eqn. 1.11].
3.19
3.20: see [San2]
3.21
3.22
3.25
3.26
3.27
3.28
3.29: see [San1, p. 17, Lemma 2.3]
3.31
3.32
3.33
3.34-U: see [And5,  p. 13, eqn. 4.10]
3.34-t  follows from the self-duality of 3.34-U.
3.35
3.36-U: see [And5 p. 11, eqn. 4.4]
3.36-t  follows from the self-duality of 3.36-U.
3.37
3.38-b: see [San1]
3.39-b: see Chapter 3, section 1.
3.39-t: see [And4, p. 663, eqn. 5.2]
3.40
3.41
3.42
3.43
3.44-b: see [And2, p. 5291, eqn. 3.2]
3.44-t
3.45
3.46-b: see [And2, p. 5291, eqn. 3.1]
3.46-t
3.49
3.50-b
3.50-t
3.52-b
3.52-T
3.52-U
3.53
3.54
3.55
3.56
3.58
3.59
3.60
3.61
3.68
3.69
3.70
3.71
3.72
3.75
3.76
3.77
3.79-b
3.79-t
3.80
3.81
3.82
3.90
3.91
3.92
3.93
3.94-b
3.94-t
3.95
3.96-b
3.96-t
3.99-b
3.99-t
3.100
3.103
3.104
3.105a
3.107
3.109A
3.110
3.114
3.115
3.116
3.117
3.118
3.119
3.120
3.121
3.122
3.123
3.124
3.125
3.128
3.130
6.79 and 6.96
6.94 and 6.99

[And1] G. E. Andrews,  "A Polynomial Identity Which Implies the Rogers-Ramanujan Identities," Scripta Mathematica, 28 (1970), 297-305.

[And2] G. E. Andrews, "The Hard-Hexagon Model and Rogers-Ramanujan Type identities," Proc. Nat. Acad. Sci. USA, 78 (1981), no. 9, part 1, 5290-5292, September 1981.

[And3] G. E. Andrews, q-Series: Their Development and Application in Analysis, Number Theory, Combinatorics, Physics, and Computer Algebra, vol. 66 of Regional Conference Series in Mathematics.  American Mathematical Society, Providence, RI, 1986.

[And3] G. E. Andrews, "Euler's 'Examplum Memorabile Inductionis Fallacis' and q-Trinomial Coefficients," J. Amer. Math. Soc., 3 (1990), 653-669.

[And4] G. E. Andrews,  "q-Trinomial Coefficents and Rogers-Ramanujan Type Identities," in Analytic Number Theory, ed. Bruce Berndt et al., Boston: Birkhauser, 1990, 1-11.

[San1] J. P. O. Santos, "Computer Algebra and Identities of the Rogers-Ramanujan Type," Ph.D. Thesis, Pennsylvania State University, 1991.

[San2] J. P. O. Santos, "On the Combinatorics of Polynomial Generalizations of Rogers-Ramanujan Type Identities," Discrete Math. 254 (2002), 497-511.

[SS] J. P. O. Santos and A. V. Sills, "q-Pell Sequences and Two Identities of V.A. Lebesgue," Discrete Math. 257/1 (2002), 125-143.