0,2

Row sums = 1, 3, 6, 11, 19, 32, 53...(Fibonacci numbers - 2; starting with F(4)) The first few rows of the triangle are:

The first few rows of the triangle are:

1;

2, 1;

3, 2, 1;

4, 4, 2, 1;

5, 6, 5, 2, 1;

6, 9, 8, 6, 2, 1;

7, 12, 14, 10, 7, 2, 1;

8, 16, 20, 20, 12, 8, 2, 1;

9, 20, 30, 30, 27, 14, 9, 2, 1;

10, 25, 40, 50, 42, 35, 16, 10, 2, 1;

...

Row sums = (Fibonacci numbers - 2; starting 1, 3, 6...).

Column 1 = A002620; Column 2 = A006918; Column 3 = A096338.

Inverse array is A105522. - Paul Barry (pbarry(AT)wit.ie), Apr 11 2005

By columns (k = 0, 1, 2...); use partial sum operator on (bin(n, k) numbers repeated).

T(n, k)=sum{j=0..n-k, C((j+2k)/2, k)(1+(-1)^j)+C((j-1+2k)/2, k)(1-(-1)^j)/2; Riordan array (1/(1-x)^2, x/(1-x^2)). - Paul Barry (pbarry(AT)wit.ie), Apr 11 2005

Column 2: 1, 2, 5, 8, 14, 20, 30...is generated by using the partial sum operator on 1, 1, 3, 3, 6, 6, 10, 10...

Cf. A001911, A002620, A006918, A096338, A105108.

Sequence in context: A131967 A137679 A152072 this_sequence A062001 A165999 A049280

Adjacent sequences: A105435 A105436 A105437 this_sequence A105439 A105440 A105441

nonn,tabl

Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 09 2005