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 A223332 Rolling cube footprints: number of 3 X n 0..7 arrays starting with 0 where 0..7 label vertices of a cube and every array movement to a horizontal or antidiagonal neighbor moves along a corresponding cube edge. 1
 64, 243, 3969, 64827, 1059723, 17324685, 283231809, 4630406067, 75700050363, 1237579942725, 20232537609249, 330771018512907, 5407599817782603, 88405979220238365, 1445302430884160289, 23628482316968449347 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Row 3 of A223331. LINKS R. H. Hardin, Table of n, a(n) for n = 1..210 FORMULA Empirical: a(n) = 18*a(n-1) - 27*a(n-2) for n>4. Conjectures from Colin Barker, Aug 19 2018: (Start) G.f.: x*(64 - 909*x + 1323*x^2 - 54*x^3) / (1 - 18*x + 27*x^2). a(n) = (49/54)*((9-3*sqrt(6))^n + (3*(3+sqrt(6)))^n) for n>2. (End) EXAMPLE Some solutions for n=3:   0 2 6    0 4 6    0 2 6    0 1 5    0 2 3    0 1 5    0 2 6   6 7 6    6 2 3    3 7 5    5 4 6    3 7 6    5 7 3    0 4 0   3 7 6    6 2 0    6 4 6    6 2 0    6 7 3    6 7 6    6 4 6 Vertex neighbors:   0 -> 1 2 4   1 -> 0 3 5   2 -> 0 3 6   3 -> 1 2 7   4 -> 0 5 6   5 -> 1 4 7   6 -> 2 4 7   7 -> 3 5 6 CROSSREFS Cf. A223331. Sequence in context: A188863 A228687 A349109 * A340696 A333428 A197605 Adjacent sequences:  A223329 A223330 A223331 * A223333 A223334 A223335 KEYWORD nonn AUTHOR R. H. Hardin, Mar 19 2013 STATUS approved

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Last modified January 22 05:19 EST 2022. Contains 350481 sequences. (Running on oeis4.)