A230954 - OEIS

%I #17 Jun 12 2022 14:06:01

%S 4,10,24,59,162,526,2016,8978,45696,261760,1666308,11668652,89141580,

%T 737740174,6575238599,62788901290,639562492327,6921688171153,

%U 79316703841369,959397056891093,12215422719238138,163308172248420391,2287234651735371577

%N Boustrophedon transform of composite numbers.

%H Reinhard Zumkeller, <a href="/A230954/b230954.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 44-54 1996 (<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 Wikipedia, <a href="http://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(A109449(n,k)*A002808(k+1): k=0..n).

%t cc = Select[Range[max = 40], CompositeQ]; t[n_, 0] := cc[[n+1]]; t[n_, k_] := t[n, k] = t[n, k-1] + t[n-1, n-k]; a[n_] := t[n, n]; Array[a, cc // Length, 0] (* _Jean-François Alcover_, Feb 12 2016 *)

%o (Haskell)

%o a230954 n = sum $ zipWith (*) (a109449_row n) a002808_list

%o (Python)

%o from itertools import accumulate, count, islice

%o from sympy import composite

%o def A230954_gen(): # generator of terms

%o     blist = tuple()

%o     for i in count(1):

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

%o A230954_list = list(islice(A230954_gen(),40)) # _Chai Wah Wu_, Jun 12 2022

%Y Cf. A230955, A000747, A000732, A230953.

%K nonn

%O 0,1

%A _Reinhard Zumkeller_, Nov 03 2013