A000745 Boustrophedon transform of squares.

1, 5, 18, 57, 180, 617, 2400, 10717, 54544, 312353, 1988104, 13921501, 106350816, 880162337, 7844596536, 74910367309, 763030711936, 8257927397569, 94628877364936, 1144609672707741, 14573622985067744, 194834987492011649, 2728787718495477144, 39955604972310966797

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

a(n) ~ n! * (6 + Pi + 4/Pi) * exp(Pi/2) * 2^n / Pi^n. - Vaclav Kotesovec, Jun 12 2015

E.g.f.: exp(x)*(x^2 + 3*x + 1)*(1+sin(x))/cos(x). - Vaclav Kotesovec, Jun 12 2015

Mathematica

CoefficientList[Series[E^(x)*(x^2+3*x+1)*(1+Sin[x])/Cos[x], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jun 12 2015 *)
t[n_, 0] := (n + 1)^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)
a000745 n = sum $ zipWith (*) (a109449_row n) $ tail a000290_list
-- Reinhard Zumkeller, Nov 03 2013
(Python)
from itertools import accumulate, count, islice
def A000745_gen(): # generator of terms
    blist, c = tuple(), 1
    for i in count(1):
        yield (blist := tuple(accumulate(reversed(blist), initial=c)))[-1]
        c += 2*i+1
A000745_list = list(islice(A000745_gen(), 40)) # Chai Wah Wu, Jun 12 2022

Crossrefs

Cf. A000290, A000697.

Sequence in context: A335720 A093374 A258109 * A343802 A271014 A272583

Adjacent sequences: A000742 A000743 A000744 * A000746 A000747 A000748

Keyword

nonn

Author

N. J. A. Sloane

Status

approved