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 A279709 T(n,k)=Number of nXk 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards. 12
 1, 1, 2, 1, 2, 4, 2, 3, 5, 8, 3, 4, 11, 13, 16, 5, 6, 22, 42, 34, 32, 8, 9, 47, 125, 161, 89, 64, 13, 14, 102, 385, 717, 617, 233, 128, 21, 22, 224, 1195, 3245, 4121, 2364, 610, 256, 34, 35, 494, 3751, 14988, 27346, 23690, 9057, 1597, 512, 55, 56, 1089, 11823, 70220 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS R. H. Hardin, Table of n, a(n) for n = 1..221 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) = 5*a(n-1) -5*a(n-2) +2*a(n-3) k=4: [order 8] for n>9 k=5: [order 12] for n>13 k=6: [order 32] for n>33 k=7: [order 60] for n>62 Empirical for row n: n=1: a(n) = a(n-1) +a(n-2) for n>3 n=2: a(n) = 2*a(n-1) -a(n-3) n=3: a(n) = 3*a(n-1) -2*a(n-2) -a(n-3) +4*a(n-4) -a(n-5) -a(n-7) -a(n-8) n=4: [order 23] for n>25 n=5: [order 56] for n>64 EXAMPLE Table starts ...1....1......1.......2.........3..........5............8............13 ...2....2......3.......4.........6..........9...........14............22 ...4....5.....11......22........47........102..........224...........494 ...8...13.....42.....125.......385.......1195.........3751.........11823 ..16...34....161.....717......3245......14988........70220........329692 ..32...89....617....4121.....27346.....187484......1302321.......9047660 ..64..233...2364...23690....230128....2342179.....24137862.....248664928 .128..610...9057..136181...1936687...29270275....447547408....6837220721 .256.1597..34699..782826..16300179..365809911...8297886949..187983779265 .512.4181.132938.4500021.137192011.4571688626.153848240903.5168463666199 Some solutions for n=4 k=4 ..0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1 ..0..0..1..0. .0..1..1..0. .0..1..0..0. .0..1..0..1. .0..1..1..0 ..1..0..1..1. .0..0..1..1. .0..0..1..1. .0..1..0..1. .0..0..0..1 ..0..1..0..1. .0..1..0..1. .1..0..0..1. .0..1..0..1. .1..1..0..1 CROSSREFS Column 1 is A000079(n-1). Column 2 is A001519. Row 1 is A000045(n-1). Row 2 is A001611. Sequence in context: A206299 A276053 A117268 * A261880 A119538 A068309 Adjacent sequences: A279706 A279707 A279708 * A279710 A279711 A279712 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Dec 17 2016 STATUS approved

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Last modified March 22 14:39 EDT 2023. Contains 361430 sequences. (Running on oeis4.)