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 A301964 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero. 12
 1, 2, 2, 3, 5, 4, 5, 6, 13, 8, 8, 9, 16, 34, 16, 13, 14, 25, 40, 89, 32, 21, 22, 41, 64, 100, 233, 64, 34, 35, 74, 111, 169, 252, 610, 128, 55, 56, 132, 219, 311, 441, 632, 1597, 256, 89, 90, 239, 443, 749, 874, 1156, 1588, 4181, 512, 144, 145, 437, 904, 1803, 2544, 2454 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Table starts ...1....2....3....5.....8.....13.....21......34.......55........89.......144 ...2....5....6....9....14.....22.....35......56.......90.......145.......234 ...4...13...16...25....41.....74....132.....239......437.......800......1468 ...8...34...40...64...111....219....443.....904.....1860......3856......8015 ..16...89..100..169...311....749...1803....4257....10353.....25491.....62623 ..32..233..252..441...874...2544...7795...22456....66659....203926....621905 ..64..610..632.1156..2454...8705..33860..120603...444357...1715911...6574776 .128.1597.1588.3025..6906..29750.148299..655332..3014296..14863160..72345489 .256.4181.3988.7921.19427.101869.646838.3557239.20467528.129324707.802690313 LINKS R. H. Hardin, Table of n, a(n) for n = 1..880 FORMULA Empirical for column k: k=1: a(n) = 2*a(n-1) k=2: a(n) = 3*a(n-1) -a(n-2) k=3: a(n) = a(n-1) +3*a(n-2) +2*a(n-3) k=4: a(n) = 2*a(n-1) +2*a(n-2) -a(n-3) for n>4 k=5: a(n) = 2*a(n-1) +3*a(n-2) -a(n-3) -2*a(n-4) -3*a(n-5) +2*a(n-6) for n>8 k=6: [order 11] for n>12 k=7: [order 14] for n>17 Empirical for row n: n=1: a(n) = a(n-1) +a(n-2) n=2: a(n) = 2*a(n-1) -a(n-3) for n>5 n=3: a(n) = 2*a(n-1) -a(n-4) for n>6 n=4: a(n) = 2*a(n-1) +a(n-3) -a(n-4) -2*a(n-6) +a(n-7) for n>9 n=5: [order 14] for n>17 n=6: [order 27] for n>32 n=7: [order 47] for n>52 EXAMPLE Some solutions for n=5 k=4 ..0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..1..0. .0..0..1..0 ..0..1..0..1. .0..0..0..1. .0..1..0..1. .0..0..1..0. .1..1..1..0 ..0..0..0..1. .0..1..0..1. .0..1..0..1. .1..0..1..1. .1..0..1..0 ..0..1..1..1. .0..1..1..1. .1..0..1..0. .1..0..0..1. .0..1..0..1 ..0..1..0..1. .0..1..0..1. .1..0..1..1. .1..1..0..1. .0..1..0..1 CROSSREFS Column 1 is A000079(n-1). Column 2 is A001519(n+1). Row 1 is A000045(n+1). Row 2 is A301791. Sequence in context: A209762 A026408 A301790 * A334043 A301884 A302081 Adjacent sequences: A301961 A301962 A301963 * A301965 A301966 A301967 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Mar 29 2018 STATUS approved

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Last modified May 31 14:54 EDT 2023. Contains 363068 sequences. (Running on oeis4.)