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 A303314 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 4, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero. 12
 1, 2, 2, 3, 3, 4, 5, 3, 4, 8, 8, 5, 12, 6, 16, 13, 7, 17, 11, 9, 32, 21, 13, 24, 36, 19, 14, 64, 34, 23, 67, 50, 74, 34, 22, 128, 55, 37, 158, 128, 139, 165, 53, 35, 256, 89, 63, 298, 439, 410, 349, 361, 83, 56, 512, 144, 109, 595, 1085, 1799, 1221, 853, 783, 136, 90, 1024, 233 (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..3...3....5....7....13.....23......37.......63.......109........183 ...4..4..12...17...24....67....158.....298......595......1337.......2863 ...8..6..11...36...50...128....439....1085.....2431......6452......17455 ..16..9..19...74..139...410...1799....5907....16494.....53290.....184915 ..32.14..34..165..349..1221...7096...30280...102683....403872....1783894 ..64.22..53..361..853..3453..26184..148313...618149...2955145...16591424 .128.35..83..783.2180.10223.100128..746323..3851318..22515378..159560449 .256.56.136.1710.5525.30247.387892.3784002.23967605.171306353.1539204838 LINKS R. H. Hardin, Table of n, a(n) for n = 1..511 FORMULA Empirical for column k: k=1: a(n) = 2*a(n-1) k=2: a(n) = 2*a(n-1) -a(n-3) k=3: a(n) = a(n-1) +a(n-3) +a(n-4) for n>7 k=4: a(n) = a(n-1) +a(n-2) +3*a(n-3) +2*a(n-4) -a(n-5) -2*a(n-6) -a(n-7) for n>10 k=5: a(n) = a(n-1) +9*a(n-3) +2*a(n-4) +4*a(n-5) -10*a(n-6) -6*a(n-7) +4*a(n-9) for n>12 k=6: [order 8] for n>11 k=7: [order 20] for n>23 Empirical for row n: n=1: a(n) = a(n-1) +a(n-2) n=2: a(n) = a(n-1) +2*a(n-3) for n>5 n=3: a(n) = a(n-1) +3*a(n-3) +4*a(n-4) for n>7 n=4: a(n) = a(n-1) +a(n-2) +5*a(n-3) +9*a(n-4) -3*a(n-5) -7*a(n-6) -2*a(n-7) for n>11 n=5: [order 12] for n>16 n=6: [order 23] for n>28 n=7: [order 46] for n>51 EXAMPLE Some solutions for n=5 k=4 ..0..1..0..0. .0..1..1..1. .0..0..0..1. .0..1..0..0. .0..1..0..1 ..0..1..1..1. .0..1..0..1. .0..1..0..1. .0..1..1..1. .0..1..1..1 ..0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1 ..0..1..0..1. .0..1..0..1. .0..0..0..1. .0..1..0..1. .0..1..0..1 ..0..0..0..1. .0..0..0..1. .1..1..0..1. .0..1..0..1. .0..1..0..1 CROSSREFS Column 1 is A000079(n-1). Column 2 is A001611(n+1). Row 1 is A000045(n+1). Row 2 is A003229(n-1) for n>2. Sequence in context: A119446 A302680 A302515 * A076918 A162620 A304115 Adjacent sequences:  A303311 A303312 A303313 * A303315 A303316 A303317 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Apr 21 2018 STATUS approved

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Last modified September 23 20:42 EDT 2021. Contains 347617 sequences. (Running on oeis4.)