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 A067962 a(n) = F(n+2)*prod(i=1,n+1,F(i))^2 where F(i)=A000045(i) is the i-th Fibonacci number. 12
 1, 2, 12, 180, 7200, 748800, 204422400, 145957593600, 272940700032000, 1336044726656640000, 17122749216831498240000, 574502481723130428948480000, 50464872497041500009263431680000, 11605406728144633757130311383449600000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Number of binary arrangements without adjacent 1's on n X n array connected nw-se. Kitaev and Mansour give a general formula for the number of binary m X n matrices avoiding certain configurations. LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..68 Sergey Kitaev and Toufik Mansour, The problem of the pawns, Annals of Combinatorics 8 (2004) 81-91. V. Kotesovec, Non-attacking chess pieces, 6ed, 2013, p. 69, 421. FORMULA a(n) = (F(3) * F(4) * ... * F(n+1))^2 * F(n+2), where F(n) = A000045(n) is the n-th Fibonacci number. a(n) is asymptotic to C^2*((1+sqrt(5))/2)^((n+2)^2)/(5^(n+3/2)) where C=1.226742010720353244... is Fibonacci Factorial Constant, see A062073. - Vaclav Kotesovec, Oct 28 2011 a(n) = a(n-1) * A001654(n+1), n > 0. - Reinhard Zumkeller, Sep 24 2015 EXAMPLE Neighbors for n=4 (dots represent spaces, circles represent grid points): O..O..O..O .\..\..\.. ..\..\..\. O..O..O..O .\..\..\.. ..\..\..\. O..O..O..O .\..\..\.. ..\..\..\. O..O..O..O MAPLE a:= proc(n) option remember; `if`(n=0, 1, (F->       F(n+1)*F(n+2)*a(n-1))(combinat[fibonacci]))     end: seq(a(n), n=0..14);  # Alois P. Heinz, May 20 2019 MATHEMATICA Rest[Table[With[{c=Fibonacci[Range[n]]}, (Times@@Most[c])^2 Last[c]], {n, 15}]] (* Harvey P. Dale, Dec 17 2013 *) PROG (PARI) a(n)=fibonacci(n+2)*prod(i=0, n, fibonacci(i+1))^2 (Haskell) a067962 n = a067962_list !! n a067962_list = 1 : zipWith (*) a067962_list (drop 2 a001654_list) -- Reinhard Zumkeller, Sep 24 2015 CROSSREFS Cf. circle A000204, line A000045, arrays: ne-sw nw-se A067965, e-w ne-sw nw-se A067963, n-s nw-se A067964, e-w n-s nw-se A066864, e-w ne-sw n-s nw-se A063443, n-s A067966, e-w n-s A006506, toruses: bare A002416, ne-sw nw-se A067960, ne-sw n-s nw-se A067959, e-w ne-sw n-s nw-se A067958, n-s A067961, e-w n-s A027683, e-w ne-sw n-s A066866. Cf. A001654, A003266. Sequence in context: A228508 A156516 A228593 * A134716 A243807 A006023 Adjacent sequences:  A067959 A067960 A067961 * A067963 A067964 A067965 KEYWORD nonn,nice AUTHOR R. H. Hardin, Feb 02 2002 EXTENSIONS Edited by Dean Hickerson, Feb 15 2002 Revised by N. J. A. Sloane following comments from Benoit Cloitre, Nov 12 2003 STATUS approved

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Last modified January 22 10:25 EST 2020. Contains 331144 sequences. (Running on oeis4.)