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A078446
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a(1)=a(2)=1; a(n)=a(n-2)/2 if a(n-2) is even, a(n)=a(n-1)+a(n-2) otherwise.
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9
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1, 1, 2, 3, 1, 4, 5, 2, 7, 1, 8, 9, 4, 13, 2, 15, 1, 16, 17, 8, 25, 4, 29, 2, 31, 1, 32, 33, 16, 49, 8, 57, 4, 61, 2, 63, 1, 64, 65, 32, 97, 16, 113, 8, 121, 4, 125, 2, 127, 1, 128, 129, 64, 193, 32, 225, 16, 241, 8, 249, 4, 253, 2, 255, 1, 256, 257, 128, 385, 64, 449, 32, 481, 16, 497
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OFFSET
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1,3
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COMMENTS
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LINKS
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FORMULA
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a(n^2)=2^n-1; a(n^2+1)=1; a(n^2+2)=2^n; a(n^2+3)=2^n+1; a(n^2+4)=2^(n-1); a(n^2+5)=3*2^n+1 ...; inequality : a(n)/2^sqrt(n) <2
Sum(k=1, n^2, a(k)) = 2*(n-2)*2^n + n*(n+1)/2 + 4
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MAPLE
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a:= proc(n) option remember;
if n < 3 then 1
elif `mod`(procname(n-2), 2) = 0 then procname(n-2)/2
else procname(n-1) + procname(n-2)
fi
end:
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MATHEMATICA
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a[n_]:= a[n]= If[n<3, 1, If[EvenQ[a[n-2]], a[n-2]/2, a[n-1]+a[n-2]]];
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PROG
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(PARI) a(n) = if(n<3, 1, if(a(n-2)%2==0, a(n-2)/2, a(n-1) + a(n-2) )); \\ G. C. Greubel, Nov 07 2019
(Sage)
@CachedFunction
def a(n):
if (n<3): return 1
elif (a(n-2)%2==0): return a(n-2)/2
else: return a(n-1) + a(n-2)
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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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