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A000733
Boustrophedon transform of partition numbers 1, 1, 1, 2, 3, 5, 7, ...
3
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
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.
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
KEYWORD
nonn
STATUS
approved