A230955 Boustrophedon transform of nonprimes.

1, 5, 15, 40, 114, 371, 1422, 6334, 32238, 184655, 1175454, 8231308, 62882262, 520416569, 4638303786, 44292536061, 451160065069, 4882696090609, 55951575728713, 676777708544967, 8617001415386120, 115200823068725262, 1613460678695102980, 23624702309844184487

Offset: 0

Author

Reinhard Zumkeller, Nov 03 2013

Keywords

• nonn

Links

• 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 44-54 1996 (Abstract, pdf, ps).
• Wikipedia, Boustrophedon transform
• Index entries for sequences related to boustrophedon transform

Crossrefs

Cf. A230954, A000747, A000732, A230953.

Programs

Haskell

a230955 n = sum $ zipWith (*) (a109449_row n) a018252_list

Mathematica

cc = Select[Range[max = 40], !PrimeQ[#]&]; 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 *)

Python

from itertools import accumulate, count, islice
from sympy import composite
def A230955_gen(): # generator of terms
    yield 1
    blist = (1,)
    for i in count(1):
        yield (blist := tuple(accumulate(reversed(blist),initial=composite(i))))[-1]
A230955_list = list(islice(A230955_gen(),40)) # Chai Wah Wu, Jun 12 2022

Formula

a(n) = Sum_{k=0..n} A109449(n,k)*A018252(k+1).