A208532 Mirror image of triangle in A125185; unsigned version of A120058.

1, 2, 1, 3, 4, 2, 4, 9, 10, 4, 5, 16, 28, 24, 8, 6, 25, 60, 80, 56, 16, 7, 36, 110, 200, 216, 128, 32, 8, 49, 182, 420, 616, 560, 288, 64, 9, 64, 280, 784, 1456, 1792, 1408, 640, 128, 10, 81, 408, 1344, 3024, 4704, 4992, 3456, 1408, 256

Offset: 0

Author

Philippe Deléham, Feb 27 2012

Keywords

• easy
• nonn
• tabl

Comments

Subtriangle of the triangle given by (1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.

Equals A007318*A134309*A097806 as infinite lower triangular matrix.

Row sums are powers of 3 (A000244).

Diagonal sums are powers of 2 (A000079).

Examples

			Triangle begins :
1
2, 1
3, 4, 2
4, 9, 10, 4
5, 16, 28, 24, 8
6, 25, 60, 80, 56, 16
7, 36, 110, 200, 216, 128, 32
8, 49, 182, 420, 616, 560, 288, 64
9, 64, 280, 784, 1456, 1792, 1408, 640, 128
10, 81, 408, 1344, 3024, 4704, 4992, 3456, 1408, 256
Triangle (1, 1, -1, 1, 0, 0, 0, ...) DELTA (0, 1, 1, 0, 0, 0, ...) begins :
1
1, 0
2, 1, 0
3, 4, 2, 0
4, 9, 10, 4, 0
5, 16, 28, 24, 8, 0
6, 25, 60, 80, 56, 16, 0
		

Crossrefs

Cf. Columns: A000027, A000290, A006331, A112742.

Cf. Diagonals: A011782, 2*A045623,

Formula

T(n,k) = 2*T(n-1,k) + 2*T(n-1,k-1) - T(n-2,k) - 2*T(n-1,k-1), T(0,0) = T(1,1) = 1, T(n,k) = 0 if k<0 or if k>n.

G.f.: (1-y*x)/((1-x)*(1-(1+2*y)*x)).

Sum_{k, 0<=k<=n} T(n,k)*x^k = A083085(n), A084567(n), A000012(n), A000027(n+1), A000244(n), A083065(n), A083076(n) for x = -3, -2, -1, 0, 1, 2, 3 respectively.