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 A000738 Boustrophedon transform (first version) of Fibonacci numbers 0,1,1,2,3,... 7
 0, 1, 3, 8, 25, 85, 334, 1497, 7635, 43738, 278415, 1949531, 14893000, 123254221, 1098523231, 10490117340, 106851450165, 1156403632189, 13251409502982, 160286076269309, 2040825708462175, 27283829950774822 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..400 Peter Luschny, An old operation on sequences: the Seidel transform J. Millar, N. J. A. Sloane and N. E. Young, A new operation on sequences: the Boustrophedon on transform, J. Combin. Theory, 17A 44-54 1996 (Abstract, pdf, ps). N. J. A. Sloane, Transforms Wikipedia, Boustrophedon_transform FORMULA E.g.f.: (2/sqrt(5)) * exp(x/2) * sinh((sqrt(5)/2)*x) * (sin(x)+1) / cos(x). - Alois P. Heinz, Feb 08 2011 a(n) ~ 4*(exp(sqrt(5)*Pi/2)-1) * (2*n/Pi)^(n+1/2) * exp(Pi/4-n-sqrt(5)*Pi/4) / sqrt(5). - Vaclav Kotesovec, Oct 05 2013 a(n) = sum(A109449(n,k)*A000045(k): k=0..n). - Reinhard Zumkeller, Nov 03 2013 MAPLE read(transforms); with(combinat): F:=fibonacci; [seq(F(n), n=0..50)]; BOUS2(%); MATHEMATICA FullSimplify[CoefficientList[Series[(2/Sqrt[5]) * E^(x/2) * (E^(Sqrt[5]/2*x)/2 - E^(-Sqrt[5]/2*x)/2) * (Sin[x]+1) / Cos[x], {x, 0, 20}], x]* Range[0, 20]!] (* Vaclav Kotesovec after Alois P. Heinz, Oct 05 2013 *) t[n_, 0] := Fibonacci[n]; t[n_, k_] := t[n, k] = t[n, k-1] + t[n-1, n-k]; a[n_] := t[n, n]; Array[a, 30, 0] (* Jean-François Alcover, Feb 12 2016 *) PROG (Haskell) a000738 n = sum \$ zipWith (*) (a109449_row n) a000045_list -- Reinhard Zumkeller, Nov 03 2013 CROSSREFS Cf. A000045, A000687, A092073, A000744. Sequence in context: A006372 A151426 A045900 * A148798 A148799 A148800 Adjacent sequences:  A000735 A000736 A000737 * A000739 A000740 A000741 KEYWORD nonn AUTHOR EXTENSIONS Entry revised by N. J. A. Sloane, Mar 16 2011 STATUS approved

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Last modified January 20 03:32 EST 2019. Contains 319323 sequences. (Running on oeis4.)