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 A231997 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with no element having a strict majority of its horizontal and antidiagonal neighbors equal to one 14
 4, 6, 9, 16, 32, 25, 39, 121, 156, 64, 81, 406, 1024, 800, 169, 168, 1225, 5778, 8464, 4000, 441, 361, 3916, 28900, 80511, 70225, 20228, 1156, 780, 12769, 155496, 674041, 1129755, 582169, 101808, 3025, 1681, 41180, 863041, 6257919, 15594601, 15851094 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Table starts .....4........6.........16...........39..............81...............168 .....9.......32........121..........406............1225..............3916 ....25......156.......1024.........5778...........28900............155496 ....64......800.......8464........80511..........674041...........6257919 ...169.....4000......70225......1129755........15594601.........245403000 ...441....20228.....582169.....15851094.......362293156........9716967198 ..1156...101808....4826809....222394359......8404672329......383555570610 ..3025...513400...40018276...3120433160....195072388900....15154710590391 ..7921..2586980..331786225..43782113196...4526898777801...598600429698510 .20736.13039568.2750792704.614302069661.105058031047524.23646568415709520 LINKS R. H. Hardin, Table of n, a(n) for n = 1..418 FORMULA Empirical for column k: k=1: a(n) = 2*a(n-1) +2*a(n-2) -a(n-3) k=2: a(n) = 3*a(n-1) +12*a(n-2) -5*a(n-3) -19*a(n-4) +2*a(n-5) +4*a(n-6) k=3: a(n) = 9*a(n-1) -3*a(n-2) -25*a(n-3) +9*a(n-4) +3*a(n-5) -a(n-6) k=4: [order 14] k=5: [order 36] k=6: [order 90] for n>91 Empirical for row n: n=1: a(n) = a(n-1) +3*a(n-3) +3*a(n-4) +3*a(n-5) +3*a(n-6) -2*a(n-8) -a(n-9) n=2: [order 15] n=3: [order 36] for n>38 EXAMPLE Some solutions for n=4 k=4 ..0..0..0..1..1....1..0..0..1..1....0..0..1..0..0....1..0..0..0..0 ..0..0..0..0..1....0..0..0..0..0....0..0..0..1..1....0..0..0..0..0 ..0..1..0..1..0....0..1..1..0..1....1..0..0..0..0....0..1..0..0..0 ..1..0..1..0..0....0..0..0..1..1....1..0..1..1..0....0..0..0..1..0 ..0..1..0..0..1....1..0..0..0..0....0..0..0..0..1....1..0..0..0..1 CROSSREFS Column 1 is A007598(n+2) Column 3 is A217022(n+1) Sequence in context: A225377 A036667 A056016 * A220144 A346591 A152002 Adjacent sequences: A231994 A231995 A231996 * A231998 A231999 A232000 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Nov 16 2013 STATUS approved

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Last modified March 30 14:20 EDT 2023. Contains 361622 sequences. (Running on oeis4.)