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A000734 Boustrophedon transform of 1,1,2,4,8,16,32,... 5
1, 2, 5, 15, 49, 177, 715, 3255, 16689, 95777, 609875, 4270695, 32624329, 269995377, 2406363835, 22979029335, 234062319969, 2533147494977, 29027730898595, 351112918079175, 4470508510495609, 59766296291090577 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of A062272. - Paul Barry, Jan 21 2005

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.: (1+exp(2x))(sec(x)+tan(x))/2. - Paul Barry, Jan 21 2005

a(n) ~ n! * (1+exp(Pi)) * (2/Pi)^(n+1). - Vaclav Kotesovec, Oct 07 2013

MATHEMATICA

CoefficientList[Series[(1+E^(2*x))*(Sec[x]+Tan[x])/2, {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 07 2013 *)

t[n_, 0] := If[n == 0, 1, 2^(n-1)]; 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

(Sage) # Algorithm of L. Seidel (1877)

def A000734_list(n) :

    A = {-1:0, 0:1}; R = []

    k = 0; e = 1; Bm = 1

    for i in range(n) :

        Am = Bm

        A[k + e] = 0

        e = -e

        for j in (0..i) :

            Am += A[k]

            A[k] = Am

            k += e

        Bm += Bm

        R.append(A[e*i//2]/2)

    return R

A000734_list(22) # Peter Luschny, Jun 02 2012

(Haskell)

a000734 n = sum $ zipWith (*) (a109449_row n) (1 : a000079_list)

-- Reinhard Zumkeller, Nov 04 2013

CROSSREFS

Cf. A109449, A000079, A000752.

Sequence in context: A149942 A149943 A079146 * A148366 A005751 A202182

Adjacent sequences:  A000731 A000732 A000733 * A000735 A000736 A000737

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Simon Plouffe

STATUS

approved

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Last modified June 25 20:26 EDT 2017. Contains 288730 sequences.