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A135416
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a(n) = A036987(n)*(n+1)/2.
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31
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1, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
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listen;
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OFFSET
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1,3
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COMMENTS
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Guy Steele defines a family of 36 integer sequences, denoted here by GS(i,j) for 1 <= i, j <= 6, as follows. a[1]=1; a[2n] = i-th term of {0,1,a[n],a[n]+1,2a[n],2a[n]+1}; a[2n+1] = j-th term of {0,1,a[n],a[n]+1,2a[n],2a[n]+1}. The present sequence is GS(1,5).
The full list of 36 sequences:
GS(1,5) = A135416 (the present sequence)
(with a(0)=1): Moebius transform of A038712.
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LINKS
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FORMULA
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G.f.: sum{k>=1, 2^(k-1)*x^(2^k-1) }.
Recurrence: a(2n+1) = 2a(n), a(2n) = 0, starting a(1) = 1.
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MAPLE
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GS:=proc(i, j, M) local a, n; a:=array(1..2*M+1); a[1]:=1;
for n from 1 to M do
a[2*n] :=[0, 1, a[n], a[n]+1, 2*a[n], 2*a[n]+1][i];
a[2*n+1]:=[0, 1, a[n], a[n]+1, 2*a[n], 2*a[n]+1][j];
od: a:=convert(a, list); RETURN(a); end;
GS(1, 5, 200):
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MATHEMATICA
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i = 1; j = 5; Clear[a]; a[1] = 1; a[n_?EvenQ] := a[n] = {0, 1, a[n/2], a[n/2]+1, 2*a[n/2], 2*a[n/2]+1}[[i]]; a[n_?OddQ] := a[n] = {0, 1, a[(n-1)/2], a[(n-1)/2]+1, 2*a[(n-1)/2], 2*a[(n-1)/2]+1}[[j]]; Array[a, 105] (* Jean-François Alcover, Sep 12 2013 *)
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PROG
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(PARI)
A048298(n) = if(!n, 0, if(!bitand(n, n-1), n, 0));
(Python)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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