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A096273
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a(0)=0, then a(n)=a(n-1)+(n-1) if n is odd, a(n)=a(n/2)+n/2 otherwise.
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2
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0, 0, 1, 3, 3, 7, 6, 12, 7, 15, 12, 22, 12, 24, 19, 33, 15, 31, 24, 42, 22, 42, 33, 55, 24, 48, 37, 63, 33, 61, 48, 78, 31, 63, 48, 82, 42, 78, 61, 99, 42, 82, 63, 105, 55, 99, 78, 124, 48, 96, 73, 123, 63, 115, 90, 144, 61, 117, 90, 148, 78, 138, 109, 171, 63, 127, 96, 162, 82
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OFFSET
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0,4
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LINKS
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FORMULA
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a(n) mod 2 = A095190(n); a(2n) mod 2 = a(2n+1) mod 2 = A010060(n); a(3n) = 0 mod 3.
G.f. g(x) satisfies g(x) = (1+x)*g(x^2)+x^2*(3*x+1)/(x^2-1)^2. - Robert Israel, Jan 20 2021
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MAPLE
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f:= proc(n) option remember;
if n::odd then procname(n-1)+n-1 else procname(n/2)+n/2 fi
end proc:
f(0):= 0:
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MATHEMATICA
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a[0] = 0; a[n_] := a[n] = If[OddQ[n], a[n - 1] + n - 1, a[n/2] + n/2]; Array[a, 100, 0] (* Amiram Eldar, Jul 28 2023 *)
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PROG
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(PARI) a(n)=if(n<1, 0, if(n%2, a(n-1)+n-1, a(n/2)+(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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