A230953 Boustrophedon transform of odd primes, cf. A065091.

3, 8, 20, 53, 154, 505, 1944, 8651, 44046, 252271, 1605874, 11245261, 85907084, 710970323, 6336648426, 60510526207, 616355168958, 6670526004559, 76438597647616, 924584128977111, 11772170758462928, 157382330019694067, 2204239468545788024, 32275035859881159165

Offset

0,1

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

Formula

a(n) = Sum_{k=0..n} A109449(n,k)*A000040(k+2).

E.g.f.: (sec(x) + tan(x)) * Sum_{k>=0} prime(k+2)*x^k/k!. - Ilya Gutkovskiy, Jun 26 2018

Mathematica

t[n_, 0] := Prime[n+2]; 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 *)

Prog

(Haskell)
a230953 n = sum $ zipWith (*) (a109449_row n) $ tail a000040_list
(Python)
from itertools import accumulate, count, islice
from sympy import prime
def A230953_gen(): # generator of terms
    blist = tuple()
    for i in count(2):
        yield (blist := tuple(accumulate(reversed(blist), initial=prime(i))))[-1]
A230953_list = list(islice(A230953_gen(), 40)) # Chai Wah Wu, Jun 12 2022

Crossrefs

Cf. A000747, A230956, A230954, A230955.

Sequence in context: A027220 A305823 A333679 * A026995 A018035 A271843

Adjacent sequences: A230950 A230951 A230952 * A230954 A230955 A230956

Keyword

nonn

Author

Reinhard Zumkeller, Nov 03 2013

Status

approved