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A000697
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Boustrophedon transform of 1, 1, 4, 9, 16, ...
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4
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1, 2, 7, 26, 89, 316, 1243, 5564, 28321, 162160, 1032051, 7226636, 55206161, 456886912, 4072080587, 38885496092, 396084390849, 4286637591872, 49121248360291, 594159600856332, 7565074996215025, 101137602761945440
(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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a(n) ~ n! * (4 + exp(Pi/2)*Pi*(2 + Pi)) * 2^n / Pi^(n+1). - Vaclav Kotesovec, Jun 12 2015
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MATHEMATICA
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t[n_, 0] := If[n==0, 1, n^2]; 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)
a000697 n = sum $ zipWith (*) (a109449_row n) (1 : tail a000290_list)
(Python)
from itertools import accumulate, count, islice
def A000697_gen(): # generator of terms
yield 1
blist, m = (1, ), 1
for i in count(1):
yield (blist := tuple(accumulate(reversed(blist), initial=m)))[-1]
m += 2*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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