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A000746 Boustrophedon transform of triangular numbers. 4
1, 4, 13, 39, 120, 407, 1578, 7042, 35840, 205253, 1306454, 9148392, 69887664, 578392583, 5155022894, 49226836114, 501420422112, 5426640606697, 62184720675718, 752172431553308, 9576956842743904, 128034481788227195 (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

a(n) = Sum_{k=0..n} A109449(n,k)*(k + 1)*(k + 2)/2. - Reinhard Zumkeller, Nov 03 2013

E.g.f.: (sec(x) + tan(x))*exp(x)*(x^2 + 4*x + 2)/2. - Sergei N. Gladkovskii, Oct 30 2014

a(n) ~ n! * (Pi^2 + 8*Pi + 8) * exp(Pi/2) * 2^(n-1) / Pi^(n+1). - Vaclav Kotesovec, Jun 12 2015

MATHEMATICA

t[n_, 0] := (n + 1) (n + 2)/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)

a000746 n = sum $ zipWith (*) (a109449_row n) $ tail a000217_list

-- Reinhard Zumkeller, Nov 03 2013

CROSSREFS

Cf. A000217, A000718, A109449.

Sequence in context: A290929 A121192 A133409 * A271012 A272581 A342159

Adjacent sequences:  A000743 A000744 A000745 * A000747 A000748 A000749

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified October 17 17:21 EDT 2021. Contains 348065 sequences. (Running on oeis4.)