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A214126
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a(2n)=a(n-1)+a(n) and a(2n+1)=a(n+1) for n>=1, with a(0)=a(1)=1.
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2
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1, 1, 2, 2, 3, 2, 4, 3, 5, 2, 5, 4, 6, 3, 7, 5, 8, 2, 7, 5, 7, 4, 9, 6, 10, 3, 9, 7, 10, 5, 12, 8, 13, 2, 10, 7, 9, 5, 12, 7, 12, 4, 11, 9, 13, 6, 15, 10, 16, 3, 13, 9, 12, 7, 16, 10, 17, 5, 15, 12, 17, 8, 20, 13, 21, 2, 15, 10, 12, 7, 17, 9, 16, 5, 14, 12
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OFFSET
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0,3
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COMMENTS
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LINKS
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FORMULA
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a(0) = a(1) = 1, for n>=1: a(2*n) = a(n-1)+a(n) and a(2*n+1) = a(n+1).
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EXAMPLE
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a(2^n+1) = 2 because a(2) = 2 and a(2*n+1) = a(n+1).
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MAPLE
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a:= proc(n) local r;
a(n):= `if`(n<2, 1, `if`(irem(n, 2, 'r')=0, a(r-1)+a(r), a(r+1)))
end:
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MATHEMATICA
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a[0] = a[1] = 1;
a[n_] := a[n] = If[EvenQ[n], a[n/2-1] + a[n/2], a[(n-1)/2+1]];
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PROG
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(Python)
a = [1]*(77*2)
for n in range(1, 77):
a[2*n ]=a[n-1]+a[n]
a[2*n+1]=a[n+1]
print(str(a[n-1]), end=', ')
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CROSSREFS
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Cf. A120562: same formula, seed {0,1}, first term removed.
Cf. A082498: same formula, seed {1,0}, first term removed.
Cf. A214127: same formula, seed {1,2}.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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