A000674 Boustrophedon transform of 1, 2, 2, 2, 2, ...

1, 3, 7, 16, 43, 138, 527, 2346, 11943, 68418, 435547, 3050026, 23300443, 192835698, 1718682167, 16412205306, 167173350543, 1809239622978, 20732358910387, 250773962554186, 3192953259262243, 42686640718266258, 597853508941160207

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

a(n) = Sum_{k=0..n} A109449(n,k)*A040000(k). - Reinhard Zumkeller, Nov 04 2013

E.g.f.: (sec(x) + tan(x))*(2*exp(x) - 1). - Sergei N. Gladkovskii, Oct 28 2014

Binomial convolution of A000111 and A040000. - Michael Somos, Oct 30 2014

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

Example

G.f. = 1 + 3*x + 7*x^2 + 16*x^3 + 43*x^4 + 138*x^5 + 527*x^6 + 2346*x^7 + ...

Mathematica

With[{nn=30}, CoefficientList[Series[(Sec[x]+Tan[x])(2Exp[x]-1), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Oct 04 2015 *)

Prog

(Haskell)
a000674 n = sum $ zipWith (*) (a109449_row n) (1 : repeat 2)
-- Reinhard Zumkeller, Nov 04 2013
(Python)
from itertools import accumulate, islice
def A000674_gen(): # generator of terms
    yield 1
    blist = (1, )
    while True:
        yield (blist := tuple(accumulate(reversed(blist), initial=2)))[-1]
A000674_list = list(islice(A000674_gen(), 30)) # Chai Wah Wu, Jun 11 2022

Crossrefs

Cf. A000111, A040000, A109449.

Sequence in context: A018023 A144977 A058300 * A129045 A217358 A323692

Adjacent sequences: A000671 A000672 A000673 * A000675 A000676 A000677

Keyword

nonn

Author

N. J. A. Sloane, Simon Plouffe

Extensions

More terms from Sean A. Irvine, Feb 20 2011

Status

approved