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Tutte had a series of papers that may qualify:

MR0130841 (24 #A695) Tutte, W. T. A census of planar triangulations. Canad. J. Math. 14 1962 21–38.

MR0137657 (25 #1108) Tutte, W. T. A census of Hamiltonian polygons. Canad. J. Math. 14 1962 402–417.

MR0142470 (26 #39) Tutte, W. T. A census of slicings. Canad. J. Math. 14 1962 708–722.

MR0146823 (26 #4343) Tutte, W. T. A census of planar maps. Canad. J. Math. 15 1963 249–271.

In Figure 8 of the last paper, he illustrates the rooted bicubic maps with $2n$ vertices for $n\le4$, according to the review by G. de B. Robinson.