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A092090
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Boustrophedon transform of Fibonacci numbers 1, 2, 3, 5, 8, ...
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1
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1, 3, 8, 22, 67, 229, 897, 4023, 20512, 117516, 748031, 5237959, 40014097, 331156423, 2951484420, 28184585550, 287085799927, 3106996356945, 35603555478689, 430652619722011, 5483239453957132, 73305511708044652, 1026690239891085363, 15033060056592047307
(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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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
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MAPLE
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read transforms; with(combinat, fibonacci): a := [seq(fibonacci(i), i=2..30)]: BOUS2(a);
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PROG
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(Python)
from itertools import accumulate, islice
def A092090_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
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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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