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Search: id:A135416
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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
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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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(1,1) = A000007
GS(1,2) = A000035
GS(1,3) = A036987
GS(1,4) = A007814
GS(1,5) = A135416 (the present sequence)
GS(1,6) = A135481
GS(2,1) = A135528
GS(2,2) = A000012
GS(2,3) = A000012
GS(2,4) = A091090
GS(2,5) = A135517
GS(2,6) = A135521
GS(3,1) = A036987
GS(3,2) = A000012
GS(3,3) = A000012
GS(3,4) = A000120
GS(3,5) = A048896
GS(3,6) = A038573
GS(4,1) = A135523
GS(4,2) = A001511
GS(4,3) = A008687
GS(4,4) = A070939
GS(4,5) = A135529
GS(4,6) = A135533
GS(5,1) = A048298
GS(5,2) = A006519
GS(5,3) = A080100
GS(5,4) = A087808
GS(5,5) = A053644
GS(5,6) = A000027
GS(6,1) = A135534
GS(6,2) = A038712
GS(6,3) = A135540
GS(6,4) = A135542
GS(6,5) = A054429
GS(6,6) = A003817
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EXAMPLE
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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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CROSSREFS
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Sequence in context: A132349 A123391 A076260 this_sequence A134309 A051516 A127391
Adjacent sequences: A135413 A135414 A135415 this_sequence A135417 A135418 A135419
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), based on a message from Guy Steele and D. E. Knuth, Mar 01 2008
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