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

Author

Reinhard Zumkeller, Nov 05 2013

Keywords

• nonn

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

Crossrefs

Cf. A005843, A000754.

Programs

Haskell

a231200 n = sum $ zipWith (*) (a109449_row n) $ [0, 2 ..]

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 *)

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

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