A062161 Boustrophedon transform of n mod 2.

0, 1, 2, 4, 12, 36, 142, 624, 3192, 18256, 116282, 814144, 6219972, 51475776, 458790022, 4381112064, 44625674352, 482962852096, 5534347077362, 66942218896384, 852334810990332, 11394877025289216

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, 17A 44-54 1996 (Abstract, pdf, ps).

Wikipedia, Boustrophedon transform

Index entries for sequences related to boustrophedon transform

Formula

a(2n) = A009747(n), a(2n+1) = A002084(n).

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

a(n) = Sum{k, k>=0} binomial(n, 2k+1)*A000111(n-2k-1). - Philippe Deléham, Aug 28 2005

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

Mathematica

With[{nn=30}, CoefficientList[Series[(Sec[x]+Tan[x])Sinh[x], {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, Feb 16 2013 *)

Prog

(Sage) # Generalized algorithm of L. Seidel (1877)
def A062161_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
        # print [A[z] for z in (-i//2..i//2)]
        R.append(A[e*i//2])
    return R
A062161_list(10) # Peter Luschny, Jun 02 2012
(Haskell)
a062161 n = sum $ zipWith (*) (a109449_row n) $ cycle [0, 1]
-- Reinhard Zumkeller, Nov 03 2013
(Python)
from itertools import accumulate, islice
def A062161_gen(): # generator of terms
    blist, m = tuple(), 1
    while True:
        yield (blist := tuple(accumulate(reversed(blist), initial=(m := 1-m))))[-1]
A062161_list = list(islice(A062161_gen(), 40)) # Chai Wah Wu, Jun 12 2022

Crossrefs

Cf. A000035, A062272.

Sequence in context: A086647 A268600 A187119 * A195733 A046993 A282165

Adjacent sequences: A062158 A062159 A062160 * A062162 A062163 A062164

Keyword

nonn,easy

Author

Frank Ellermann, Jun 10 2001

Status

approved