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Search: id:A115265
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| A115265 |
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Correlation triangle for floor((n+3)/3). |
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+0
2
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| 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 3, 3, 3, 2, 2, 4, 4, 4, 4, 2, 3, 4, 5, 7, 5, 4, 3, 3, 5, 6, 8, 8, 6, 5, 3, 3, 6, 7, 9, 11, 9, 7, 6, 3, 4, 6, 8, 12, 12, 12, 12, 8, 6, 4, 4, 7, 9, 13, 15, 15, 15, 13, 9, 7, 4
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Row sums are A115266. Diagonal sums are A115267. T(2n,n) is A092353. T(2n,n)-T(2n,n+1)=A087508(n+1).
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FORMULA
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G.f.: (1+x+x^2)(1+xy+x^2*y^2)/((1-x^3)^2*(1-x^3*y^3)^2*(1-x^2*y)); Number triangle T(n, k)=sum{j=0..n, [j<=k]*floor((k-j+3)/3)*[j<=n-k]*floor((n-k-j+3)/3)}.
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EXAMPLE
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Triangle begins
1;
1,1;
1,2,1;
2,2,2,2;
2,3,3,3,2;
2,4,4,4,4,2;
3,4,5,7,5,4,3;
3,5,6,8,8,6,5,3;
3,6,7,9,11,9,7,6,3;
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CROSSREFS
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Sequence in context: A024939 A024937 A143977 this_sequence A105223 A025859 A031281
Adjacent sequences: A115262 A115263 A115264 this_sequence A115266 A115267 A115268
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Jan 18 2006
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