|
| |
|
|
A105438
|
|
Triangle, row sums = (Fibonacci numbers - 2).
|
|
2
| |
|
|
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, 11, 30, 55, 70, 77, 56, 44, 18, 11, 2, 1
(list; table; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
COMMENTS
| 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
|
|
|
FORMULA
| 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
|
|
|
EXAMPLE
| 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...
|
|
|
CROSSREFS
| Cf. A001911, A002620, A006918, A096338, A105108.
Sequence in context: A131967 A137679 A152072 * A062001 A181847 A165999
Adjacent sequences: A105435 A105436 A105437 * A105439 A105440 A105441
|
|
|
KEYWORD
| nonn,tabl
|
|
|
AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 09 2005
|
| |
|
|
