A000752 Boustrophedon transform of powers of 2.

1, 3, 9, 28, 93, 338, 1369, 6238, 31993, 183618, 1169229, 8187598, 62545893, 517622498, 4613366689, 44054301358, 448733127793, 4856429646978, 55650582121749, 673136951045518, 8570645832753693, 114581094529057058, 1604780986816602409, 23497612049668468078

Offset

0,2

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

N. J. A. Sloane, Transforms.

Wikipedia, Boustrophedon transform.

Index entries for sequences related to boustrophedon transform

Formula

E.g.f.: exp(2*x) (tan(x) + sec(x)).

a(n) = Sum_{k=0..n} A109449(n,k)*2^k. - Reinhard Zumkeller, Nov 03 2013

G.f.: E(0)*x/(1 - 2*x)/(1 - 3*x) + 1/(1 - 2*x), where E(k) = 1 - x^2*(k+1)*(k+2)/(x^2*(k+1)*(k+2) - 2*(x*(k+3) - 1)*(x*(k+4) -1)/E(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Jan 16 2014

a(n) ~ n! * exp(Pi) * 2^(n+2) / Pi^(n+1). - Vaclav Kotesovec, Jun 12 2015

Mathematica

t[n_, 0] := 2^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 *)
With[{nn=30}, CoefficientList[Series[Exp[2x](Tan[ x]+Sec[x]), {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, Dec 15 2018 *)

Prog

(Haskell)
a000752 n = sum $ zipWith (*) (a109449_row n) a000079_list
-- Reinhard Zumkeller, Nov 03 2013
(Python)
from itertools import accumulate, islice
def A000752_gen(): # generator of terms
    blist, m = tuple(), 1
    while True:
        yield (blist := tuple(accumulate(reversed(blist), initial=m)))[-1]
        m *= 2
A000752_list = list(islice(A000752_gen(), 40)) # Chai Wah Wu, Jun 12 2022

Crossrefs

Cf. A000079, A000734.

Column k=2 of A292975.

Sequence in context: A361763 A120985 A014323 * A047027 A366859 A148931

Adjacent sequences: A000749 A000750 A000751 * A000753 A000754 A000755

Keyword

nonn

Author

N. J. A. Sloane

Status

approved