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 A206840 Number of 2 X n 0..3 arrays avoiding the pattern z-2 z-1 z in any row, column, nw-to-se diagonal or ne-to-sw antidiagonal. 3
 1, 16, 256, 3844, 58081, 876096, 13220496, 199487376, 3010168225, 45421839376, 685391917456, 10342205764900, 156058483721569, 2354841001103616, 35533320688065600, 536179248686523456, 8090664794986628449, 122083905679560691216, 1842182367418373568064 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Column and row 2 of A206838. LINKS R. H. Hardin and Alois P. Heinz, Table of n, a(n) for n = 0..1000 (terms n = 1..210 from R. H. Hardin) Index entries for linear recurrences with constant coefficients, signature (16,-7,-120,282,-84,-42,0,7,-4,1). FORMULA a(n) = 16*a(n-1) -7*a(n-2) -120*a(n-3) +282*a(n-4) -84*a(n-5) -42*a(n-6) +7*a(n-8) -4*a(n-9) +a(n-10). a(n) = A206839(n)^2. - Mark van Hoeij, May 14 2013 G.f.: (1 + 7*x^2 - 20*x^3 + 7*x^4 + x^6) / ((1 - 16*x + 14*x^2 - 4*x^3 + x^4)*(1 - 7*x^2 + 12*x^3 + 7*x^4 - x^6)). - Colin Barker, Jul 08 2019 EXAMPLE Some solutions for n=5 ..1..3..3..1..3....3..3..1..0..0....3..3..3..3..1....2..0..2..0..3 ..2..2..1..1..3....2..1..2..1..0....1..1..3..1..1....3..1..0..1..0 MAPLE a:= n-> ((<<0|1|0|0>, <0|0|1|0>, <0|0|0|1>, <1|-2|0|4>>^n)[4\$2])^2: seq(a(n), n=0..25); # Alois P. Heinz, Oct 26 2016 PROG (PARI) Vec((1 + 7*x^2 - 20*x^3 + 7*x^4 + x^6) / ((1 - 16*x + 14*x^2 - 4*x^3 + x^4)*(1 - 7*x^2 + 12*x^3 + 7*x^4 - x^6)) + O(x^20)) \\ Colin Barker, Jul 08 2019 CROSSREFS Cf. A206838, A206839. Sequence in context: A206791 A221665 A227592 * A222932 A220107 A171290 Adjacent sequences: A206837 A206838 A206839 * A206841 A206842 A206843 KEYWORD nonn,easy AUTHOR R. H. Hardin, Feb 13 2012 EXTENSIONS a(0)=1 prepended by Alois P. Heinz, Oct 26 2016 STATUS approved

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Last modified November 30 05:38 EST 2022. Contains 358431 sequences. (Running on oeis4.)