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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

(list; graph; refs; listen; history; text; internal format)

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