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Search: id:A115268
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| A115268 |
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Correlation triangle for floor((n+4)/4). |
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+0
4
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| 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 2, 2, 3, 2, 2, 2, 3, 3, 3, 3, 2, 2, 4, 4, 4, 4, 4, 2, 2, 4, 5, 5, 5, 5, 4, 2, 3, 4, 6, 6, 8, 6, 6, 4, 3, 3, 5, 6, 7, 9, 9, 7, 6, 5, 3, 3, 6, 7, 8, 10, 12, 10, 8, 7, 6, 3, 3, 6, 8, 9, 11, 13, 13, 11, 9, 8, 6, 3, 4, 6, 9, 10, 14, 14, 16, 14, 14, 10, 9, 6, 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 A115269. Diagonal sums are A115270. T(2n,n) is A115271. T(2n,n)-T(2n,n-1) is 1,1,1,0,2,2,2,0,3,3,3,0,...
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FORMULA
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G.f.: (1+x+x^2+x^3)(1+xy+x^2*y^2+x^3*y^3)/((1-x^4)^2*(1-x^4*y^4)^2*(1-x^2*y)); Number triangle T(n, k)=sum{j=0..n, [j<=k]*floor((k-j+4)/4)*[j<=n-k]*floor((n-k-j+4)/4)}.
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EXAMPLE
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Triangle begins
1;
1,1;
1,2,1;
1,2,2,1;
2,2,3,2,2;
2,3,3,3,3,2;
2,4,4,4,4,4,2;
2,4,5,5,5,5,4,2;
3,4,6,6,8,6,6,4,3;
3,5,6,7,9,9,7,6,5,3;
3,6,7,8,10,12,10,8,7,6,3;
3,6,8,9,11,13,13,11,9,8,6,3;
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CROSSREFS
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Sequence in context: A008679 A029435 A089643 this_sequence A103610 A109705 A025848
Adjacent sequences: A115265 A115266 A115267 this_sequence A115269 A115270 A115271
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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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