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A000744 Boustrophedon transform (second version) of Fibonacci numbers 1,1,2,3,... 6
1, 2, 5, 14, 42, 144, 563, 2526, 12877, 73778, 469616, 3288428, 25121097, 207902202, 1852961189, 17694468210, 180234349762, 1950592724756, 22352145975707, 270366543452702, 3442413745494957, 46021681757269830 (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 Ser. A, 76(1) (1996), 44-54 (Abstract, pdf, ps).

J. Millar, N. J. A. Sloane and N. E. Young, A new operation on sequences: the Boustrophedon transform, J. Combin. Theory Ser. A, 76(1) (1996), 44-54.

Ludwig Seidel, Über eine einfache Entstehungsweise der Bernoulli'schen Zahlen und einiger verwandten Reihen, Sitzungsberichte der mathematisch-physikalischen Classe der königlich bayerischen Akademie der Wissenschaften zu München, volume 7 (1877), 157-187. [USA access only through the HATHI TRUST Digital Library]

Ludwig Seidel, Über eine einfache Entstehungsweise der Bernoulli'schen Zahlen und einiger verwandten Reihen, Sitzungsberichte der mathematisch-physikalischen Classe der königlich bayerischen Akademie der Wissenschaften zu München, volume 7 (1877), 157-187. [Access through ZOBODAT]

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)*A000045(k+1). - Reinhard Zumkeller, Nov 03 2013

E.g.f.: (1/10)*(sec(x)+tan(x))*((5^(1/2)+1)*exp(1/2*x*(5^(1/2)+1))+(5^(1/2)-1)*exp(1/2*x*(-5^(1/2)+1)))*5^(1/2). - Sergei N. Gladkovskii, Oct 30 2014

a(n) ~ n! * (sqrt(5) - 1 + (1+sqrt(5)) * exp(sqrt(5)*Pi/2)) * 2^(n+1) / (sqrt(5) * exp((sqrt(5)-1)*Pi/4) * Pi^(n+1)). - Vaclav Kotesovec, Jun 12 2015

EXAMPLE

G.f. = 1 + 2*x + 5*x^2 + 14*x^3 + 42*x^4 + 144*x^5 + 563*x^6 + 2526*x^7 + ...

MAPLE

read(transforms);

with(combinat):

F:=fibonacci;

[seq(F(n), n=1..50)];

BOUS2(%);

MATHEMATICA

s[k_] := SeriesCoefficient[(1 + Sin[x])/Cos[x], {x, 0, k}] k!;

b[n_, k_] := Binomial[n, k] s[n - k];

a[n_] := Sum[b[n, k] Fibonacci[k + 1], {k, 0, n}];

Array[a, 22, 0] (* Jean-François Alcover, Jun 01 2019 *)

PROG

(Haskell)

a000744 n = sum $ zipWith (*) (a109449_row n) $ tail a000045_list

-- Reinhard Zumkeller, Nov 03 2013

CROSSREFS

Cf. A000045, A000687, A000738, A092073.

Sequence in context: A149878 A148332 A000751 * A047046 A063545 A061058

Adjacent sequences:  A000741 A000742 A000743 * A000745 A000746 A000747

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

Entry revised by N. J. A. Sloane, Mar 16 2011

STATUS

approved

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Last modified August 3 13:49 EDT 2020. Contains 336198 sequences. (Running on oeis4.)