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A000752
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Boustrophedon transform of powers of 2.
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7
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1, 3, 9, 28, 93, 338, 1369, 6238, 31993, 183618, 1169229, 8187598, 62545893, 517622498, 4613366689, 44054301358, 448733127793, 4856429646978, 55650582121749, 673136951045518, 8570645832753693, 114581094529057058, 1604780986816602409, 23497612049668468078
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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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.: exp(2*x) (tan(x) + sec(x)).
a(n) = Sum_{k=0..n} A109449(n,k)*2^k. - Reinhard Zumkeller, Nov 03 2013
G.f.: E(0)*x/(1 - 2*x)/(1 - 3*x) + 1/(1 - 2*x), where E(k) = 1 - x^2*(k+1)*(k+2)/(x^2*(k+1)*(k+2) - 2*(x*(k+3) - 1)*(x*(k+4) -1)/E(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Jan 16 2014
a(n) ~ n! * exp(Pi) * 2^(n+2) / Pi^(n+1). - Vaclav Kotesovec, Jun 12 2015
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MATHEMATICA
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t[n_, 0] := 2^n; 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 *)
With[{nn=30}, CoefficientList[Series[Exp[2x](Tan[ x]+Sec[x]), {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, Dec 15 2018 *)
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PROG
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(Haskell)
a000752 n = sum $ zipWith (*) (a109449_row n) a000079_list
-- Reinhard Zumkeller, Nov 03 2013
(Python)
from itertools import accumulate, islice
def A000752_gen(): # generator of terms
blist, m = tuple(), 1
while True:
yield (blist := tuple(accumulate(reversed(blist), initial=m)))[-1]
m *= 2
A000752_list = list(islice(A000752_gen(), 40)) # Chai Wah Wu, Jun 12 2022
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CROSSREFS
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Cf. A000079, A000734.
Column k=2 of A292975.
Sequence in context: A361763 A120985 A014323 * A047027 A148931 A243599
Adjacent sequences: A000749 A000750 A000751 * A000753 A000754 A000755
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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