A000697 Boustrophedon transform of 1, 1, 4, 9, 16, ...

1, 2, 7, 26, 89, 316, 1243, 5564, 28321, 162160, 1032051, 7226636, 55206161, 456886912, 4072080587, 38885496092, 396084390849, 4286637591872, 49121248360291, 594159600856332, 7565074996215025, 101137602761945440

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

E.g.f.: (1 + exp(x)*x*(1 + x))*(sec(x) + tan(x)). - Sergei N. Gladkovskii, Oct 29 2014

a(n) ~ n! * (4 + exp(Pi/2)*Pi*(2 + Pi)) * 2^n / Pi^(n+1). - Vaclav Kotesovec, Jun 12 2015

Mathematica

t[n_, 0] := If[n==0, 1, n^2]; 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)
a000697 n = sum $ zipWith (*) (a109449_row n) (1 : tail a000290_list)
-- Reinhard Zumkeller, Nov 04 2013
(Python)
from itertools import accumulate, count, islice
def A000697_gen(): # generator of terms
    yield 1
    blist, m = (1, ), 1
    for i in count(1):
        yield (blist := tuple(accumulate(reversed(blist), initial=m)))[-1]
        m += 2*i+1
A000697_list = list(islice(A000697_gen(), 40)) # Chai Wah Wu, Jun 12 2022

Crossrefs

Cf. A000290, A000745, A109449.

Sequence in context: A363108 A300451 A212961 * A027417 A134063 A087448

Adjacent sequences: A000694 A000695 A000696 * A000698 A000699 A000700

Keyword

nonn

Author

N. J. A. Sloane, Simon Plouffe

Status

approved