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

0,2

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).

Links

Table of n, a(n) for n=0..54.

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.

Example

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,

Sequence in context: A125100 A128544 A120058 * A245334 A102756 A086614

Adjacent sequences: A208529 A208530 A208531 * A208533 A208534 A208535

Keyword

easy,nonn,tabl

Author

Philippe Deléham, Feb 27 2012

Status

approved