|
| |
|
|
A072405
|
|
Triangle of C(n,k)-C(n-2,k-1).
|
|
10
|
|
|
|
1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 3, 4, 3, 1, 1, 4, 7, 7, 4, 1, 1, 5, 11, 14, 11, 5, 1, 1, 6, 16, 25, 25, 16, 6, 1, 1, 7, 22, 41, 50, 41, 22, 7, 1, 1, 8, 29, 63, 91, 91, 63, 29, 8, 1, 1, 9, 37, 92, 154, 182, 154, 92, 37, 9, 1, 1, 10, 46, 129, 246, 336, 336, 246, 129, 46, 10, 1, 1, 11, 56
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,8
|
|
|
COMMENTS
|
Starting 1,0,1,1,1,... this is the Riordan array ((1-x+x^2)/(1-x),x/(1-x)). Its diagonal sums are A006355. Its inverse is A106509. - Paul Barry, May 04 2005
|
|
|
LINKS
|
Table of n, a(n) for n=0..80.
|
|
|
FORMULA
|
T(n, k)=T(n-1, k-1)+T(n-1, k) starting with T(2, 0)=T(2, 1)=T(2, 2)=1.
G.f.: (1-x^2y) / [1-x(1+y)]. - R. Stephan, Jan 31 2005
|
|
|
EXAMPLE
|
Rows start:
1;
1,1;
1,1,1; (key row for starting the recurrence)
1,2,2,1;
1,3,4,3,1;
1,4,7,7,4,1;
1,5,11,14,11,5,1;
|
|
|
CROSSREFS
|
Row sums give essentially A003945, A007283, or A042950. Cf. A072406 for number of odd terms in each row.
Cf. A051597, A096646, A122218.
Sequence in context: A086461 A047089 A122218 * A146565 A115594 A086623
Adjacent sequences: A072402 A072403 A072404 * A072406 A072407 A072408
|
|
|
KEYWORD
|
easy,nonn,tabl
|
|
|
AUTHOR
|
Henry Bottomley, Jun 16 2002
|
|
|
STATUS
|
approved
|
| |
|
|
