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A000751 Boustrophedon transform of partition numbers. 5
1, 2, 5, 14, 42, 143, 555, 2485, 12649, 72463, 461207, 3229622, 24671899, 204185616, 1819837153, 17378165240, 177012514388, 1915724368181, 21952583954117, 265533531724484, 3380877926676504, 45199008472762756 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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,changed

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified June 25 03:59 EDT 2022. Contains 354835 sequences. (Running on oeis4.)