A231179 Boustrophedon transform of nonnegative integers, cf. A001477.

0, 1, 4, 12, 36, 120, 462, 2058, 10472, 59976, 381770, 2673374, 20422908, 169020852, 1506427678, 14385323610, 146527700944, 1585801332848, 18171944693586, 219803766565366, 2798628476670180, 37414906698747564, 524019526485293894, 7672827408344428242

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(n) = A231200(n)/2.

a(n) = Sum_{k=1..n} k * A109449(n,k).

E.g.f.: x*exp(x)*(sec(x)+tan(x)). (After Sergei N. Gladkovskii in A000660.) - Peter Luschny, Oct 28 2014

a(n) = A000660(n) - A000111(n). - Sergei N. Gladkovskii, Oct 28 2014

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

Mathematica

a[n_] := n! SeriesCoefficient[x Exp[x] (1+Sin[x]) / Cos[x], {x, 0, n}];
Table[a[n], {n, 0, 23}] (* Jean-François Alcover, Jul 30 2018, after Peter Luschny *)

Prog

(Haskell)
a231179 n = sum $ zipWith (*) (a109449_row n) [0..]
(Python)
from itertools import count, islice, accumulate
def A231179_gen(): # generator of terms
    blist = tuple()
    for i in count(0):
        yield (blist := tuple(accumulate(reversed(blist), initial=i)))[-1]
A231179_list = list(islice(A231179_gen(), 30)) # Chai Wah Wu, Jun 11 2022

Crossrefs

Cf. A000111, A000737, A000660, A109449, A231200.

Sequence in context: A192205 A055395 A113990 * A331717 A192010 A252697

Adjacent sequences: A231176 A231177 A231178 * A231180 A231181 A231182

Keyword

nonn

Author

Reinhard Zumkeller, Nov 05 2013

Status

approved