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A000751
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Boustrophedon transform of partition numbers.
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5
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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)
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OFFSET
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0,2
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LINKS
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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).
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FORMULA
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EXAMPLE
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The array begins:
1
1 -> 2
5 <- 4 <- 2
3 -> 8 -> 12 -> 14
42 <- 39 <- 31 <- 19 <- 5
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MATHEMATICA
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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 *)
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PROG
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(Haskell)
a000751 n = sum $ zipWith (*) (a109449_row n) a000041_list
(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]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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