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 A034182 Number of not-necessarily-symmetric n X 2 crossword puzzle grids. 20
 1, 5, 15, 39, 97, 237, 575, 1391, 3361, 8117, 19599, 47319, 114241, 275805, 665855, 1607519, 3880897, 9369317, 22619535, 54608391, 131836321, 318281037, 768398399, 1855077839, 4478554081, 10812186005, 26102926095, 63018038199, 152139002497, 367296043197 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS n X 2 binary arrays with a path of adjacent 1's and no path of adjacent 0's from top row to bottom row. - R. H. Hardin, Mar 21 2002 Define a triangle with T(n,1) = T(n,n) = n*(n-1) + 1, n>=1, and its interior terms via T(r,c) = T(r-1,c) + T(r-1,c-1)+ T(r-2,c-1), 2<=c=1 - Paolo P. Lava, Jun 10 2008 (1 + 5x + 15x^2 + ...) = (1 + 2x + 2x^2 + ...) * (1 + 3x + 7x^2 + ...), where A001333 = (1, 1, 3, 7, 17, 41, ...). a(n) = (-4 + (1-sqrt(2))^(1+n) + (1+sqrt(2))^(1+n))/2. G.f.: x*(1+x)^2/((1-x)*(1 - 2*x - x^2)). - Colin Barker, May 22 2012 a(n) = A001333(n+1)-2. - R. J. Mathar, Mar 28 2013 MATHEMATICA t={0, 0}; Do[AppendTo[t, t[[-2]]+2*t[[-1]]+2], {n, 40}]; Drop[t-1, 2] (* Vladimir Joseph Stephan Orlovsky, Jan 25 2012 *) {1}~Join~NestList[{#2, 2 #2 + #1 + 4} & @@ # &, {1, 5}, 28][[All, -1]] (* Michael De Vlieger, Oct 02 2017 *) PROG (Haskell) a034182 n = a034182_list !! (n-1) a034182_list = 1 : 5 : (map (+ 4) \$    zipWith (+) a034182_list (map (* 2) \$ tail a034182_list)) -- Reinhard Zumkeller, May 23 2013 CROSSREFS Row 2 of A292357. Column sums of A059678. Cf. A001333, A034184, A034187. Sequence in context: A084447 A099035 A262295 * A132985 A022570 A152881 Adjacent sequences:  A034179 A034180 A034181 * A034183 A034184 A034185 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified December 15 15:10 EST 2019. Contains 329999 sequences. (Running on oeis4.)