A231200 Boustrophedon transform of even numbers.

0, 2, 8, 24, 72, 240, 924, 4116, 20944, 119952, 763540, 5346748, 40845816, 338041704, 3012855356, 28770647220, 293055401888, 3171602665696, 36343889387172, 439607533130732, 5597256953340360, 74829813397495128, 1048039052970587788, 15345654816688856484

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

Wikipedia, Boustrophedon_transform

Index entries for sequences related to boustrophedon transform

Formula

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

a(n) = 2*A231179(n).

E.g.f.: 2*x*exp(x)*(sec(x) + tan(x)). - Ilya Gutkovskiy, Sep 27 2017

Mathematica

T[n_, k_] := SeriesCoefficient[(1+Sin[x])/Cos[x], {x, 0, n-k}] n!/k!;
a[n_] := 2 Sum[k T[n, k], {k, 0, n}];
Table[a[n], {n, 0, 23}] (* Jean-François Alcover, Jun 28 2019 *)

Prog

(Haskell)
a231200 n = sum $ zipWith (*) (a109449_row n) $ [0, 2 ..]
(Python)
from itertools import accumulate, count, islice
def A231200_gen(): # generator of terms
    blist = tuple()
    for i in count(0, 2):
        yield (blist := tuple(accumulate(reversed(blist), initial=i)))[-1]
A231200_list = list(islice(A231200_gen(), 40)) # Chai Wah Wu, Jun 12 2022

Crossrefs

Cf. A005843, A000754.

Sequence in context: A131569 A363602 A290904 * A066973 A130495 A026070

Adjacent sequences: A231197 A231198 A231199 * A231201 A231202 A231203

Keyword

nonn

Author

Reinhard Zumkeller, Nov 05 2013

Status

approved