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 A214112 T(n,k)=Number of 0..3 colorings of an nx(k+1) array circular in the k+1 direction with new values 0..3 introduced in row major order 12
 1, 1, 4, 4, 11, 25, 10, 111, 121, 172, 31, 670, 3502, 1331, 1201, 91, 4994, 44900, 110985, 14641, 8404, 274, 34041, 825105, 3008980, 3517864, 161051, 58825, 820, 241021, 12777541, 136579852, 201647240, 111505491, 1771561, 411772, 2461, 1678940 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Table starts ....1.....1.......4........10..........31............91.............274 ....4....11.....111.......670........4994.........34041..........241021 ...25...121....3502.....44900......825105......12777541.......214404272 ..172..1331..110985...3008980...136579852....4797577911....191154162535 .1201.14641.3517864.201647240.22615881851.1801391900581.170522196557894 LINKS R. H. Hardin, Table of n, a(n) for n = 1..160 FORMULA Empirical for column k: k=1: a(n) = 8*a(n-1) -7*a(n-2) k=2: a(n) = 11*a(n-1) k=3: a(n) = 35*a(n-1) -107*a(n-2) +73*a(n-3) k=4: a(n) = 68*a(n-1) -66*a(n-2) k=5: a(n) = 200*a(n-1) -5769*a(n-2) +11744*a(n-3) +43057*a(n-4) -89856*a(n-5) +40625*a(n-6) k=6: a(n) = 416*a(n-1) -15454*a(n-2) +89758*a(n-3) +90848*a(n-4) -438718*a(n-5) +62801*a(n-6) k=7: (order 15) Empirical for row n: n=1: a(k)=3*a(k-1)+a(k-2)-3*a(k-3) n=2: a(k)=4*a(k-1)+22*a(k-2)-4*a(k-3)-21*a(k-4) n=3: a(k)=11*a(k-1)+123*a(k-2)-509*a(k-3)-1615*a(k-4)+7137*a(k-5)-19*a(k-6)-20571*a(k-7)+13176*a(k-8)+13932*a(k-9)-11664*a(k-10) n=4: (order 26) n=5: (order 71) EXAMPLE Some solutions for n=4 k=1 ..0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1 ..1..0....1..2....2..3....1..0....1..0....1..0....1..2....1..0....1..0....1..2 ..0..1....0..1....3..1....0..1....2..3....2..1....3..0....0..2....2..3....3..1 ..1..2....1..0....1..0....1..0....3..2....3..0....0..1....1..3....3..1....0..2 CROSSREFS Column 1 is A034494(n-1) Column 2 is A001020(n-1) Row 1 is A006342(n-1) Sequence in context: A302516 A254205 A048223 * A211950 A014012 A273391 Adjacent sequences:  A214109 A214110 A214111 * A214113 A214114 A214115 KEYWORD nonn,tabl AUTHOR R. H. Hardin Jul 04 2012 STATUS approved

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Last modified May 21 18:55 EDT 2022. Contains 353926 sequences. (Running on oeis4.)