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A000745 Boustrophedon transform of squares. 3
1, 5, 18, 57, 180, 617, 2400, 10717, 54544, 312353, 1988104, 13921501, 106350816, 880162337, 7844596536, 74910367309, 763030711936, 8257927397569, 94628877364936, 1144609672707741, 14573622985067744 (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 on transform, J. Combin. Theory, 17A 44-54 1996 (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-Fran├žois Alcover, Feb 12 2016 *)

PROG

(Haskell)

a000745 n = sum $ zipWith (*) (a109449_row n) $ tail a000290_list

-- Reinhard Zumkeller, Nov 03 2013

CROSSREFS

Cf. A000290, A000697.

Sequence in context: A001793 A093374 A258109 * A271014 A272583 A247717

Adjacent sequences:  A000742 A000743 A000744 * A000746 A000747 A000748

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified December 7 23:12 EST 2016. Contains 278900 sequences.