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A000732
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Boustrophedon transform of 1 & primes: 1,2,3,5,7,...
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5
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1, 3, 8, 22, 66, 222, 862, 3838, 19542, 111894, 712282, 4987672, 38102844, 315339898, 2810523166, 26838510154, 273374835624, 2958608945772, 33903161435148, 410085034127000, 5221364826476796, 69804505809732988
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refs;
listen;
history;
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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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a(n) = Sum_{k=0..n} A109449(n,k)*A008578(k+1). - Reinhard Zumkeller, Nov 04 2013
E.g.f.: (sec(x) + tan(x))*(1 + Sum_{k>=1} prime(k)*x^k/k!). - Ilya Gutkovskiy, Apr 23 2019
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MATHEMATICA
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t[n_, 0] := If[n==0, 1, Prime[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 *)
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PROG
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(Haskell)
a000732 n = sum $ zipWith (*) (a109449_row n) a008578_list
(Python)
from itertools import accumulate, count, islice
from sympy import prime
def A000732_gen(): # generator of terms
yield 1
blist = (1, )
for i in count(1):
yield (blist := tuple(accumulate(reversed(blist), initial=prime(i))))[-1]
A000732_list = list(islice(A000732_gen(), 40)) # Chai Wah Wu, Jun 12 2022
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CROSSREFS
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Cf. A000747, A230953, A230954, A230955.
Sequence in context: A117420 A003101 A064443 * A092090 A011958 A260661
Adjacent sequences: A000729 A000730 A000731 * A000733 A000734 A000735
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane and Simon Plouffe
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STATUS
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approved
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