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A000737 Boustrophedon transform of natural numbers, cf. A000027. 4
1, 3, 8, 21, 60, 197, 756, 3367, 17136, 98153, 624804, 4375283, 33424512, 276622829, 2465449252, 23543304919, 239810132288, 2595353815825, 29740563986500, 359735190398875, 4580290700420064, 61233976084442741 (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

E.g.f.: (1+x)(tan x + sec x) exp(x).

a(n) ~ n! * (Pi+2)*exp(Pi/2)*2^(n+1)/Pi^(n+1). - Vaclav Kotesovec, Oct 02 2013

MATHEMATICA

CoefficientList[Series[(1+x)*(Tan[x]+1/Cos[x])* E^x, {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 02 2013 *)

t[n_, 0] := n + 1; 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

(Sage) # Algorithm of L. Seidel (1877)

def A000737_list(n) :

    R = []; A = {-1:0, 0:0}

    k = 0; e = 1

    for i in range(n) :

        Am = i+1

        A[k + e] = 0

        e = -e

        for j in (0..i) :

            Am += A[k]

            A[k] = Am

            k += e

        print [A[z] for z in (-i//2..i//2)]

        R.append(A[e*i//2])

    return R

A000737_list(10) # Peter Luschny, Jun 02 2012

(Haskell)

a000737 n = sum $ zipWith (*) (a109449_row n) [1..]

-- Reinhard Zumkeller, Nov 05 2013

CROSSREFS

Cf. A231179.

Sequence in context: A273720 A018037 A018038 * A192235 A148769 A156291

Adjacent sequences:  A000734 A000735 A000736 * A000738 A000739 A000740

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified October 23 04:22 EDT 2018. Contains 316519 sequences. (Running on oeis4.)