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A000733
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Boustrophedon transform of partition numbers 1, 1, 1, 2, 3, 5, 7, ...
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3
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1, 2, 4, 10, 30, 101, 394, 1760, 8970, 51368, 326991, 2289669, 17491625, 144760655, 1290204758, 12320541392, 125496010615, 1358185050788, 15563654383395, 188254471337718, 2396930376564860, 32044598671291610
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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LINKS
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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
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EXAMPLE
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The array begins:
1
1 -> 2
4 <- 3 <- 1
2 -> 6 -> 9 -> 10
30 <- 28 <- 22 <- 13 <- 3
- John Cerkan, Jan 26 2017
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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Cf. A000041, A000751, A109449, A230957.
Sequence in context: A328358 A007558 A094957 * A092073 A274232 A112846
Adjacent sequences: A000730 A000731 A000732 * A000734 A000735 A000736
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KEYWORD
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nonn,changed
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AUTHOR
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N. J. A. Sloane, Simon Plouffe
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STATUS
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approved
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