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A000732 Boustrophedon transform of 1 & primes: 1,2,3,5,7,... 6

%I #35 Jun 12 2022 12:00:55

%S 1,3,8,22,66,222,862,3838,19542,111894,712282,4987672,38102844,

%T 315339898,2810523166,26838510154,273374835624,2958608945772,

%U 33903161435148,410085034127000,5221364826476796,69804505809732988

%N Boustrophedon transform of 1 & primes: 1,2,3,5,7,...

%H Reinhard Zumkeller, <a href="/A000732/b000732.txt">Table of n, a(n) for n = 0..400</a>

%H Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/SeidelTransform">An old operation on sequences: the Seidel transform</a>.

%H 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 (<a href="http://neilsloane.com/doc/bous.txt">Abstract</a>, <a href="http://neilsloane.com/doc/bous.pdf">pdf</a>, <a href="http://neilsloane.com/doc/bous.ps">ps</a>).

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Boustrophedon_transform">Boustrophedon transform</a>.

%H <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a>

%F a(n) = Sum_{k=0..n} A109449(n,k)*A008578(k+1). - _Reinhard Zumkeller_, Nov 04 2013

%F E.g.f.: (sec(x) + tan(x))*(1 + Sum_{k>=1} prime(k)*x^k/k!). - _Ilya Gutkovskiy_, Apr 23 2019

%t 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 *)

%o (Haskell)

%o a000732 n = sum $ zipWith (*) (a109449_row n) a008578_list

%o (Python)

%o from itertools import accumulate, count, islice

%o from sympy import prime

%o def A000732_gen(): # generator of terms

%o yield 1

%o blist = (1,)

%o for i in count(1):

%o yield (blist := tuple(accumulate(reversed(blist),initial=prime(i))))[-1]

%o A000732_list = list(islice(A000732_gen(),40)) # _Chai Wah Wu_, Jun 12 2022

%Y Cf. A000747, A230953, A230954, A230955.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_ and _Simon Plouffe_

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Last modified March 29 10:22 EDT 2024. Contains 371268 sequences. (Running on oeis4.)