A062272 Boustrophedon transform of (n+1) mod 2.

1, 1, 2, 5, 12, 41, 152, 685, 3472, 19921, 126752, 887765, 6781632, 56126201, 500231552, 4776869245, 48656756992, 526589630881, 6034272215552, 72989204937125, 929327412759552, 12424192360405961, 174008703107274752

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
(Python)
from itertools import accumulate, islice
def A062272_gen(): # generator of terms
    blist, m = tuple(), 0
    while True:
        yield (blist := tuple(accumulate(reversed(blist), initial=(m := 1-m))))[-1]
A062272_list = list(islice(A062272_gen(), 40)) # Chai Wah Wu, Jun 12 2022

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: A005664 A364761 A009739 * A215789 A127137 A172239

Adjacent sequences: A062269 A062270 A062271 * A062273 A062274 A062275

Keyword

nonn,easy

Author

Frank Ellermann, Jun 16 2001

Status

approved