This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A223692 #16 Jul 23 2025 04:24:21 %S A223692 16,48,256,144,432,4096,432,2304,3888,65536,1296,12384,37008,34992, %T A223692 1048576,3888,66816,363600,595584,314928,16777216,11664,361440, %U A223692 3788640,10817856,9594000,2834352,268435456,34992,1958400,40075632,223096320,324280368,154616832,25509168,4294967296 %N A223692 T(n,k)=Petersen graph (8,2) coloring a rectangular array: number of nXk 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 antidiagonal neighbor moves along an edge of this graph. %H A223692 R. H. Hardin, <a href="/A223692/b223692.txt">Table of n, a(n) for n = 1..218</a> %F A223692 Empirical for column k: %F A223692 k=1: a(n) = 16*a(n-1) %F A223692 k=2: a(n) = 9*a(n-1) %F A223692 k=3: a(n) = 24*a(n-1) -127*a(n-2) %F A223692 k=4: a(n) = 59*a(n-1) -1103*a(n-2) +7621*a(n-3) -16900*a(n-4) %F A223692 k=5: [order 7] for n>8 %F A223692 k=6: [order 17] for n>18 %F A223692 k=7: [order 37] for n>39 %F A223692 Empirical for row n: %F A223692 n=1: a(n) = 3*a(n-1) %F A223692 n=2: a(n) = 8*a(n-1) -11*a(n-2) -16*a(n-3) for n>4 %F A223692 n=3: a(n) = [order 10] for n>12 %F A223692 n=4: a(n) = [order 24] for n>27 %F A223692 n=5: a(n) = [order 56] for n>61 %e A223692 Table starts: %e A223692 16, 48, 144, 432, 1296, ... %e A223692 256, 432, 2304, 12384, 66816, ... %e A223692 4096, 3888, 37008, 363600, 3788640, ... %e A223692 65536, 34992, 595584, 10817856, 223096320, ... %e A223692 1048576, 314928, 9594000, 324280368, 13402129824, ... %e A223692 16777216, 2834352, 154616832, 9762152544, 814399853760, ... %e A223692 268435456, 25509168, 2492365968, 294583794768, 49817845241568, ... %e A223692 4294967296, 229582512, 40180445568, 8901308553408, 3059068970173824, ... %e A223692 Some solutions for n=3 k=4 %e A223692 ..2..1..9..1....6..5..4..5....6.14..6.14....4..3..2.10....2..3..4..3 %e A223692 ..2..1..9.11....4..5..6.14...12.14..8.14....2.10..2.10....4..3.11.13 %e A223692 ..9.11..9.15....6..7..6.14....8..0..8..0....8.10..8.10...11.13.11..9 %Y A223692 Column 1 is A001025 %Y A223692 Column 2 is 48*9^(n-1) %Y A223692 Row 1 is A188825(n+1) %K A223692 nonn,tabl %O A223692 1,1 %A A223692 _R. H. Hardin_, Mar 25 2013