A000751 Boustrophedon transform of partition numbers.

1, 2, 5, 14, 42, 143, 555, 2485, 12649, 72463, 461207, 3229622, 24671899, 204185616, 1819837153, 17378165240, 177012514388, 1915724368181, 21952583954117, 265533531724484, 3380877926676504, 45199008472762756

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

Formula

a(n) = Sum_{k=0..n} A109449(n,k)*A000041(k). - Reinhard Zumkeller, Nov 03 2013

Example

The array begins:
                   1
               1  ->   2
           5  <-   4  <-   2
       3  ->   8  ->  12  ->  14
  42  <-  39  <-  31  <-  19  <-   5
- John Cerkan, Jan 26 2017

Mathematica

t[n_, 0] := PartitionsP[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 *)

Prog

(Haskell)
a000751 n = sum $ zipWith (*) (a109449_row n) a000041_list
-- Reinhard Zumkeller, Nov 03 2013
(Python)
from itertools import accumulate, count, islice
from sympy import npartitions
def A000751_gen(): # generator of terms
    blist = tuple()
    for i in count(0):
        yield (blist := tuple(accumulate(reversed(blist), initial=npartitions(i))))[-1]
A000751_list = list(islice(A000751_gen(), 40)) # Chai Wah Wu, Jun 12 2022

Crossrefs

Cf. A000733, A230957.

Sequence in context: A149877 A149878 A148332 * A000744 A047046 A063545

Adjacent sequences: A000748 A000749 A000750 * A000752 A000753 A000754

Keyword

nonn

Author

N. J. A. Sloane

Status

approved