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A000674
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Boustrophedon transform of 1, 2, 2, 2, 2, ...
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2
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1, 3, 7, 16, 43, 138, 527, 2346, 11943, 68418, 435547, 3050026, 23300443, 192835698, 1718682167, 16412205306, 167173350543, 1809239622978, 20732358910387, 250773962554186, 3192953259262243, 42686640718266258, 597853508941160207
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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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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) ~ n! * (2*exp(Pi/2)-1) * 2^(n+2) / Pi^(n+1). - Vaclav Kotesovec, Jun 12 2015
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EXAMPLE
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G.f. = 1 + 3*x + 7*x^2 + 16*x^3 + 43*x^4 + 138*x^5 + 527*x^6 + 2346*x^7 + ...
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MATHEMATICA
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With[{nn=30}, CoefficientList[Series[(Sec[x]+Tan[x])(2Exp[x]-1), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Oct 04 2015 *)
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PROG
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(Haskell)
a000674 n = sum $ zipWith (*) (a109449_row n) (1 : repeat 2)
(Python)
from itertools import accumulate, islice
def A000674_gen(): # generator of terms
yield 1
blist = (1, )
while True:
yield (blist := tuple(accumulate(reversed(blist), initial=2)))[-1]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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