A000754 Boustrophedon transform of odd numbers.

1, 4, 12, 33, 96, 317, 1218, 5425, 27608, 158129, 1006574, 7048657, 53847420, 445643681, 3971876930, 37928628529, 386337833232, 4181155148673, 47912508680086, 579538956964241, 7378919177090244, 98648882783190305

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

From Reinhard Zumkeller, Nov 02 2013: (Start)

a(n) = Sum_{k=0..n} A116666(n+1,k)*A000111(n-k).

a(n) = Sum_{k=0..n} A109449(n,k)*(2*k + 1). (End)

E.g.f.: (sec(x) + tan(x))*exp(x)*(2*x + 1). - Sergei N. Gladkovskii, Oct 30 2014

a(n) ~ n! * (Pi+1) * exp(Pi/2) * 2^(n+2) / Pi^(n+1). - Vaclav Kotesovec, Oct 30 2014

Mathematica

CoefficientList[Series[(Sec[x]+Tan[x])*E^x*(2*x+1), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Oct 30 2014 after Sergei N. Gladkovskii *)
t[n_, 0] := 2n + 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-François Alcover, Feb 12 2016 *)

Prog

(Haskell)
a000754 n = sum $ zipWith (*) (a109449_row n) [1, 3 ..]
-- Reinhard Zumkeller, Nov 02 2013
(Python)
from itertools import accumulate, count, islice
def A000754_gen(): # generator of terms
    blist = tuple()
    for i in count(1, 2):
        yield (blist := tuple(accumulate(reversed(blist), initial=i)))[-1]
A000754_list = list(islice(A000754_gen(), 40)) # Chai Wah Wu, Jun 12 2022

Crossrefs

Cf. A005408.

Sequence in context: A219092 A135254 A326804 * A317974 A119683 A331834

Adjacent sequences: A000751 A000752 A000753 * A000755 A000756 A000757

Keyword

nonn,nice,easy

Author

N. J. A. Sloane

Status

approved