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A000734
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Boustrophedon transform of 1,1,2,4,8,16,32,...
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5
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1, 2, 5, 15, 49, 177, 715, 3255, 16689, 95777, 609875, 4270695, 32624329, 269995377, 2406363835, 22979029335, 234062319969, 2533147494977, 29027730898595, 351112918079175, 4470508510495609, 59766296291090577
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graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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COMMENTS
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Binomial transform of A062272. - Paul Barry, Jan 21 2005
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LINKS
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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
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FORMULA
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E.g.f.: (1 + exp(2*x))*(sec(x) + tan(x))/2. - Paul Barry, Jan 21 2005
a(n) ~ n! * (1 + exp(Pi)) * (2/Pi)^(n+1). - Vaclav Kotesovec, Oct 07 2013
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MATHEMATICA
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CoefficientList[Series[(1+E^(2*x))*(Sec[x]+Tan[x])/2, {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 07 2013 *)
t[n_, 0] := If[n == 0, 1, 2^(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-François Alcover, Feb 12 2016 *)
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PROG
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(Sage) # Algorithm of L. Seidel (1877)
def A000734_list(n) :
A = {-1:0, 0:1}; R = []
k = 0; e = 1; Bm = 1
for i in range(n) :
Am = Bm
A[k + e] = 0
e = -e
for j in (0..i) :
Am += A[k]
A[k] = Am
k += e
Bm += Bm
R.append(A[e*i//2]/2)
return R
A000734_list(22) # Peter Luschny, Jun 02 2012
(Haskell)
a000734 n = sum $ zipWith (*) (a109449_row n) (1 : a000079_list)
-- Reinhard Zumkeller, Nov 04 2013
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CROSSREFS
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Cf. A109449, A000079, A000752.
Sequence in context: A149942 A149943 A079146 * A148366 A005751 A202182
Adjacent sequences: A000731 A000732 A000733 * A000735 A000736 A000737
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Simon Plouffe
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STATUS
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approved
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