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A000754
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Boustrophedon transform of odd numbers.
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5
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1, 4, 12, 33, 96, 317, 1218, 5425, 27608, 158129, 1006574, 7048657, 53847420, 445643681, 3971876930, 37928628529, 386337833232, 4181155148673, 47912508680086, 579538956964241, 7378919177090244, 98648882783190305
(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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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).
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FORMULA
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a(n) = Sum_{k=0..n} A109449(n,k)*(2*k + 1). (End)
a(n) ~ n! * (Pi+1) * exp(Pi/2) * 2^(n+2) / Pi^(n+1). - Vaclav Kotesovec, Oct 30 2014
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MATHEMATICA
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t[n_, 0] := 2n + 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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(Haskell)
a000754 n = sum $ zipWith (*) (a109449_row n) [1, 3 ..]
(Python)
from itertools import accumulate, count, islice
def A000754_gen(): # generator of terms
blist = tuple()
for i in count(1, 2):
yield (blist := tuple(accumulate(reversed(blist), initial=i)))[-1]
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CROSSREFS
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KEYWORD
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nonn,nice,easy
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AUTHOR
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STATUS
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approved
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