login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Index entries for sequences related to 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-Fran├žois 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

N. J. A. Sloane.

EXTENSIONS

Entry revised by N. J. A. Sloane, Mar 16 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified February 23 13:38 EST 2018. Contains 299581 sequences. (Running on oeis4.)