A000733 Boustrophedon transform of partition numbers 1, 1, 1, 2, 3, 5, 7, ...

1, 2, 4, 10, 30, 101, 394, 1760, 8970, 51368, 326991, 2289669, 17491625, 144760655, 1290204758, 12320541392, 125496010615, 1358185050788, 15563654383395, 188254471337718, 2396930376564860, 32044598671291610

Offset

0,2

Links

John Cerkan, Table of n, a(n) for n = 0..482

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

Example

The array begins:
                   1
               1  ->   2
           4  <-   3  <-   1
       2  ->   6  ->   9  ->  10
  30  <-  28  <-  22  <-  13  <-   3
- John Cerkan, Jan 26 2017

Mathematica

t[n_, 0] := If[n == 0, 1, PartitionsP[n-1]]; 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)
a000733 n = sum $ zipWith (*) (a109449_row n) (1 : a000041_list)
-- Reinhard Zumkeller, Nov 04 2013
(Python)
from itertools import count, accumulate, islice
from sympy import npartitions
def A000733_gen(): # generator of terms
    yield 1
    blist = (1, )
    for i in count(0):
        yield (blist := tuple(accumulate(reversed(blist), initial=npartitions(i))))[-1]
A000733_list = list(islice(A000733_gen(), 40)) # Chai Wah Wu, Jun 12 2022

Crossrefs

Cf. A000041, A000751, A109449, A230957.

Sequence in context: A328358 A007558 A094957 * A092073 A274232 A360322

Adjacent sequences: A000730 A000731 A000732 * A000734 A000735 A000736

Keyword

nonn

Author

N. J. A. Sloane, Simon Plouffe

Status

approved