|
|
A000734
|
|
Boustrophedon transform of 1,1,2,4,8,16,32,...
|
|
5
|
|
|
1, 2, 5, 15, 49, 177, 715, 3255, 16689, 95777, 609875, 4270695, 32624329, 269995377, 2406363835, 22979029335, 234062319969, 2533147494977, 29027730898595, 351112918079175, 4470508510495609, 59766296291090577
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
|
|
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).
|
|
FORMULA
|
E.g.f.: (1 + exp(2*x))*(sec(x) + tan(x))/2. - Paul Barry, Jan 21 2005
|
|
MATHEMATICA
|
CoefficientList[Series[(1+E^(2*x))*(Sec[x]+Tan[x])/2, {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 07 2013 *)
t[n_, 0] := If[n == 0, 1, 2^(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
|
(Sage) # Algorithm of L. Seidel (1877)
A = {-1:0, 0:1}; R = []
k = 0; e = 1; Bm = 1
for i in range(n) :
Am = Bm
A[k + e] = 0
e = -e
for j in (0..i) :
Am += A[k]
A[k] = Am
k += e
Bm += Bm
R.append(A[e*i//2]/2)
return R
(Haskell)
a000734 n = sum $ zipWith (*) (a109449_row n) (1 : a000079_list)
(Python)
from itertools import count, accumulate, islice
def A000734_gen(): # generator of terms
yield 1
blist, m = (1, ), 1
while True:
yield (blist := tuple(accumulate(reversed(blist), initial=m)))[-1]
m *= 2
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|