A115281 Correlation triangle for the sequence 2-0^n.

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

Offset: 0

Author

Paul Barry, Jan 19 2006

Keywords

• easy
• nonn
• tabl

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.

From Mats Granvik, Jul 06 2010: (Start)

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)

Examples

			Triangle begins
1;
2,2;
2,5,2;
2,6,6,2;
2,6,9,6,2;
2,6,10,10,6,2;
		

Programs

Mathematica

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 *)

Formula

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))}.

Extensions

a(65)-a(66) from Mats Granvik, Jan 06 2016