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 A135416 A036987(n)*(n+1)/2. 30

%I

%S 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,

%T 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,

%U 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

%N A036987(n)*(n+1)/2.

%C 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).

%C The full list of 36 sequences:

%C GS(1,1) = A000007

%C GS(1,2) = A000035

%C GS(1,3) = A036987

%C GS(1,4) = A007814

%C GS(1,5) = A135416 (the present sequence)

%C GS(1,6) = A135481

%C GS(2,1) = A135528

%C GS(2,2) = A000012

%C GS(2,3) = A000012

%C GS(2,4) = A091090

%C GS(2,5) = A135517

%C GS(2,6) = A135521

%C GS(3,1) = A036987

%C GS(3,2) = A000012

%C GS(3,3) = A000012

%C GS(3,4) = A000120

%C GS(3,5) = A048896

%C GS(3,6) = A038573

%C GS(4,1) = A135523

%C GS(4,2) = A001511

%C GS(4,3) = A008687

%C GS(4,4) = A070939

%C GS(4,5) = A135529

%C GS(4,6) = A135533

%C GS(5,1) = A048298

%C GS(5,2) = A006519

%C GS(5,3) = A080100

%C GS(5,4) = A087808

%C GS(5,5) = A053644

%C GS(5,6) = A000027

%C GS(6,1) = A135534

%C GS(6,2) = A038712

%C GS(6,3) = A135540

%C GS(6,4) = A135542

%C GS(6,5) = A054429

%C GS(6,6) = A003817

%C (with a(0)=1): Moebius transform of A038712.

%F G.f.: sum{k>=1, 2^(k-1)*x^(2^k-1) }.

%e GS:=proc(i,j,M) local a,n; a:=array(1..2*M+1); a[1]:=1;

%e for n from 1 to M do

%e a[2*n] :=[0,1,a[n],a[n]+1,2*a[n],2*a[n]+1][i];

%e a[2*n+1]:=[0,1,a[n],a[n]+1,2*a[n],2*a[n]+1][j];

%e od: a:=convert(a,list); RETURN(a); end;

%e GS(1,5,200):

%Y Equals A048298(n+1)/2. Cf. A036987, A182660.

%K nonn

%O 1,3

%A _N. J. A. Sloane_, based on a message from Guy Steele and D. E. Knuth, Mar 01 2008

%E Formula and comments by Ralf Stephan, Nov 27 2010

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Last modified May 22 10:40 EDT 2013. Contains 225526 sequences.