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A092090
Boustrophedon transform of Fibonacci numbers 1, 2, 3, 5, 8,...
1
1, 3, 8, 22, 67, 229, 897, 4023, 20512, 117516, 748031, 5237959, 40014097, 331156423, 2951484420, 28184585550, 287085799927, 3106996356945, 35603555478689, 430652619722011, 5483239453957132, 73305511708044652, 1026690239891085363, 15033060056592047307
OFFSET
0,2
LINKS
C. A. Church and M. Bicknell,Exponential generating functions for Fibonacci identities,Fibonacci Quarterly, 11(3) (1973), 275-281.
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.
FORMULA
E.g.f.: (sec(x) + tan(x))*(a^2*exp(a*x) - b^2*exp(b*x))/(a - b), where a = (1 + sqrt(5))/2 and b = (1 - sqrt(5))/2. -Petros Hadjicostas,Feb 16 2021
MAPLE
read transforms; with(combinat, fibonacci): a:= [seq(fibonacci(i), i=2..30)]: BOUS2(a);
PROG
(Python)
from itertools import accumulate, islice
defA092090_gen(): # generator of terms
blist, a, b = tuple(), 1, 2
while True:
yield (blist:= tuple(accumulate(reversed(blist), initial=a)))[-1]
a, b = b, a+b
A092090_list = list(islice(A092090_gen(), 40)) #Chai Wah Wu,Jun 12 2022
CROSSREFS
Cf.A000744(which uses BOUS2),A062122(which uses Fibonacci numbers with an error in them),A092073.
KEYWORD
nonn
AUTHOR
N. J. A. Sloane,Apr 01 2004
STATUS
approved