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A115281
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Correlation triangle for the sequence 2-0^n.
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0
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1, 2, 2, 2, 5, 2, 2, 6, 6, 2, 2, 6, 9, 6, 2, 2, 6, 10, 10, 6, 2, 2, 6, 10, 13, 10, 6, 2, 2, 6, 10, 14, 14, 10, 6, 2, 2, 6, 10, 14, 17, 14, 10, 6, 2, 2, 6, 10, 14, 18, 18, 14, 10, 6, 2, 2, 6, 10, 14, 18, 21, 18, 14, 10
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Row sums are (n+1)^2 (A000290(n+1)). Diagonal sums are the Molien series A007980. T(2n,n) is 4n+1 (A016813), the partial sums of (2-0^n)^2. T(2,n)-T(2n,n+1) is 3-2*0^n.
Contribution from Mats Granvik (mats.granvik(AT)abo.fi), Jul 06 2010: (Start)
If seen as an infinite square array:
1, 2, 2, 2
2, 5, 6, 6
2, 6, 9, 10
2, 6, 10, 13
then the matrix inverse contains the same values, only signed and in reversed order:
13, -10, 6, -2
-10, 9, -6, 2
6, -6, 5, -2
-2, 2, -2, 1
(End)
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FORMULA
| G.f.: (1+x)(1+x*y)/((1-x)(1-x*y)(1-x^2*y)); Number triangle T(n, k)=sum{j=0..n, [j<=k]*(2-0^(k-j))*[j<=n-k]*(2-0^(n-k-j))}.
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EXAMPLE
| Triangle begins
1;
2,2;
2,5,2;
2,6,6,2;
2,6,9,6,2;
2,6,10,10,6,2;
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CROSSREFS
| Sequence in context: A088885 A121358 A112659 * A130155 A113516 A120642
Adjacent sequences: A115278 A115279 A115280 * A115282 A115283 A115284
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Jan 19 2006
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