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A208532 Mirror image of triangle in A125185; unsigned version of A120058. 2
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified June 24 21:50 EDT 2021. Contains 345433 sequences. (Running on oeis4.)