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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, 6, 2
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OFFSET
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0,2
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COMMENTS
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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.
If seen as a 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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LINKS
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FORMULA
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G.f.: (1+x)(1+x*y)/((1-x)(1-x*y)(1-x^2*y)).
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
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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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MATHEMATICA
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Flatten[Table[Table[If[n - k + 1 == k, 4*(n - k + 1 - 1) + 1, If[n - k + 1 > k, 4*(k - 1) + 2, 4*(n - k + 1 - 1) + 2]], {k, 1, n}], {n, 1, 11}]] (* Mats Granvik, Jan 06 2016 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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