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A062272 Boustrophedon transform of (n+1) mod 2. 8
1, 1, 2, 5, 12, 41, 152, 685, 3472, 19921, 126752, 887765, 6781632, 56126201, 500231552, 4776869245, 48656756992, 526589630881, 6034272215552, 72989204937125, 929327412759552, 12424192360405961, 174008703107274752 (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 transform, J. Combin. Theory Ser. A, 76(1) (1996), 44-54 (Abstract, pdf, ps).

J. Millar, N. J. A. Sloane, and N. E. Young, A new operation on sequences: the Boustrophedon transform, J. Combin. Theory Ser. A, 76(1) (1996), 44-54.

Ludwig Seidel, Über eine einfache Entstehungsweise der Bernoulli'schen Zahlen und einiger verwandten Reihen, Sitzungsberichte der mathematisch-physikalischen Classe der königlich bayerischen Akademie der Wissenschaften zu München, volume 7 (1877), 157-187. [USA access only through the HATHI TRUST Digital Library]

Ludwig Seidel, Über eine einfache Entstehungsweise der Bernoulli'schen Zahlen und einiger verwandten Reihen, Sitzungsberichte der mathematisch-physikalischen Classe der königlich bayerischen Akademie der Wissenschaften zu München, volume 7 (1877), 157-187. [Access through ZOBODAT]

Wikipedia, Boustrophedon transform.

Index entries for sequences related to boustrophedon transform

FORMULA

E.g.f.: (sec(x)+tan(x))cosh(x); a(n)=(A000667(n)+A062162(n))/2. - Paul Barry, Jan 21 2005

a(n) = Sum{k, k>=0} binomial(n, 2k)*A000111(n-2k). - Philippe Deléham, Aug 28 2005

a(n) = sum(A109449(n,k) * (1 - n mod 2): k=0..n). - Reinhard Zumkeller, Nov 03 2013

MATHEMATICA

s[n_] = Mod[n+1, 2]; t[n_, 0] := s[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

(Sage) # Generalized algorithm of L. Seidel (1877)

def A062272_list(n) :

    R = []; A = {-1:0, 0:0}

    k = 0; e = 1

    for i in range(n) :

        Am = 1 if e == 1 else 0

        A[k + e] = 0

        e = -e

        for j in (0..i) :

            Am += A[k]

            A[k] = Am

            k += e

        R.append(A[e*i//2])

    return R

A062272_list(10) # Peter Luschny, Jun 02 2012

(Haskell)

a062272 n = sum $ zipWith (*) (a109449_row n) $ cycle [1, 0]

-- Reinhard Zumkeller, Nov 03 2013

CROSSREFS

A000734 (binomial transform), a(2n+1)= A003719(n), a(2n)= A000795(n),

Cf. A062161 (n mod 2).

Row sums of A162170 minus A000035. - Mats Granvik, Jun 27 2009

Cf. A059841.

Sequence in context: A140440 A005664 A009739 * A215789 A127137 A172239

Adjacent sequences:  A062269 A062270 A062271 * A062273 A062274 A062275

KEYWORD

nonn,easy,changed

AUTHOR

Frank Ellermann, Jun 16 2001

STATUS

approved

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Last modified October 21 01:18 EDT 2019. Contains 328291 sequences. (Running on oeis4.)