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A223437 Generalized Petersen graph (8,2) coloring a rectangular array: number of nX5 0..15 arrays where 0..15 label nodes of a graph with edges 0,1 0,8 8,14 8,10 1,2 1,9 9,15 9,11 2,3 2,10 10,12 3,4 3,11 11,13 4,5 4,12 12,14 5,6 5,13 13,15 6,7 6,14 7,0 7,15 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

%I A223437 #6 Jul 23 2025 04:09:37
%S A223437 1296,40160,1562176,67182208,3049973040,142702806112,6790055219264,
%T A223437 326095786136512,15740601974728144,761894144429277728,
%U A223437 36933075864379992960,1791784217341289032832,86964938378374308543408
%N A223437 Generalized Petersen graph (8,2) coloring a rectangular array: number of nX5 0..15 arrays where 0..15 label nodes of a graph with edges 0,1 0,8 8,14 8,10 1,2 1,9 9,15 9,11 2,3 2,10 10,12 3,4 3,11 11,13 4,5 4,12 12,14 5,6 5,13 13,15 6,7 6,14 7,0 7,15 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.
%C A223437 Column 5 of A223440
%H A223437 R. H. Hardin, <a href="/A223437/b223437.txt">Table of n, a(n) for n = 1..210</a>
%F A223437 Empirical: a(n) = 62*a(n-1) +97*a(n-2) -43361*a(n-3) +169107*a(n-4) +9430075*a(n-5) -42692985*a(n-6) -944380223*a(n-7) +4270354567*a(n-8) +50259902237*a(n-9) -223620107693*a(n-10) -1517318142163*a(n-11) +6782196814489*a(n-12) +26682637399469*a(n-13) -124450548676359*a(n-14) -271316347782785*a(n-15) +1405146906215354*a(n-16) +1486735261657557*a(n-17) -9731248121419764*a(n-18) -3199983254595948*a(n-19) +40528119973374804*a(n-20) -5730916061514328*a(n-21) -98589639864853568*a(n-22) +43705272486463008*a(n-23) +135607659234364992*a(n-24) -89468393018269056*a(n-25) -98957223312948992*a(n-26) +87411803248288256*a(n-27) +31094370745832448*a(n-28) -42403903770849280*a(n-29) +555544355516416*a(n-30) +9031467111268352*a(n-31) -2014501576998912*a(n-32) -534258356224000*a(n-33) +246552412291072*a(n-34) -28053544108032*a(n-35) +759655563264*a(n-36)
%e A223437 Some solutions for n=3
%e A223437 .14.12.14.12.10...14..8..0..7..0...14..8.10.12..4...10.12.10.12.14
%e A223437 ..8.14..8.14..8....8..0..7.15..7....6.14..8.14.12....2.10..2.10..8
%e A223437 ..0..8.14..8..0....0..7.15..7..6...14..8.14.12..4...10.12.10..2.10
%K A223437 nonn
%O A223437 1,1
%A A223437 _R. H. Hardin_ Mar 20 2013