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 A223233 T(n,k)=Rolling icosahedron footprints: number of nXk 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves along an icosahedral edge 11
 1, 5, 12, 25, 65, 144, 125, 785, 845, 1728, 625, 7445, 25225, 10985, 20736, 3125, 75665, 492365, 812225, 142805, 248832, 15625, 753005, 11043445, 32837285, 26157625, 1856465, 2985984, 78125, 7540985, 236027705, 1697263985, 2191464605, 842416625 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Table starts ............1.............5................25.................125 ...........12............65...............785................7445 ..........144...........845.............25225..............492365 .........1728.........10985............812225............32837285 ........20736........142805..........26157625..........2191464605 .......248832.......1856465.........842416625........146259564725 ......2985984......24134045.......27130395625.......9761484584045 .....35831808.....313742585......873746350625.....651489782832965 ....429981696....4078653605....28139386665625...43480983274973885 ...5159780352...53022496865...906241361740625.2901957882023749205 ..61917364224..689292459245.29185902861015625 .743008370688.8960801970185 LINKS R. H. Hardin, Table of n, a(n) for n = 1..97 FORMULA Empirical for column k: k=1: a(n) = 12*a(n-1) k=2: a(n) = 13*a(n-1) k=3: a(n) = 35*a(n-1) -90*a(n-2) k=4: a(n) = 73*a(n-1) -423*a(n-2) +351*a(n-3) k=5: [order 11] k=6: [order 26] Empirical for row n: n=1: a(n) = 5*a(n-1) n=2: a(n) = 7*a(n-1) +30*a(n-2) for n>3 n=3: a(n) = 18*a(n-1) +103*a(n-2) -552*a(n-3) +540*a(n-4) for n>5 n=4: a(n) = [order 12] for n>13 EXAMPLE Some solutions for n=3 k=4 ..0..6..0..5....0..5..6..5....0..7..0..1....0..1..3..1....0..1..0..7 ..0..6.10..5....0..5..6..5....3..7..0..7....3..7..3..9....0..7..0..7 ..0..5.10..4....6..2..6..5....3..7..5..7....3..9.11..7....3..1..3..7 Vertex neighbors: 0 -> 1 2 5 6 7 1 -> 0 2 3 7 8 2 -> 0 1 4 6 8 3 -> 1 7 8 9 11 4 -> 2 6 8 9 10 5 -> 0 6 7 10 11 6 -> 0 2 4 5 10 7 -> 0 1 3 5 11 8 -> 1 2 3 4 9 9 -> 3 4 8 10 11 10 -> 4 5 6 9 11 11 -> 3 5 7 9 10 CROSSREFS Column 1 is A001021(n-1) Column 2 is 5*13^(n-1) Row 1 is A000351(n-1) Sequence in context: A301748 A108201 A289586 * A038254 A223321 A073095 Adjacent sequences: A223230 A223231 A223232 * A223234 A223235 A223236 KEYWORD nonn,tabl AUTHOR R. H. Hardin Mar 18 2013 STATUS approved

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Last modified August 14 16:54 EDT 2024. Contains 375166 sequences. (Running on oeis4.)