|
| |
|
|
A152198
|
|
Triangle read by rows, A007318 rows repeated
|
|
13
| |
|
|
1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1, 4, 6, 4, 1, 1, 4, 6, 4, 1, 1, 5, 10, 10, 5, 1, 1, 5, 10, 10, 5, 1, 1, 6, 15, 20, 15, 6, 1, 1, 6, 15, 20, 15, 6, 1, 1, 7, 21, 35, 35, 21, 7, 1, 1, 7, 21, 35, 35, 21, 7, 1, 1, 8, 28, 56, 70, 56, 28, 8, 1, 1, 8, 28, 56, 70, 56, 28, 8, 1
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,8
|
|
|
COMMENTS
| Eigensequence of the triangle = A051163: (1, 2, 5, 12, 30, 76,...)
Another version of A152815 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 13 2008]
Row sums : A016116(n) ; Diagonal sums : A000931(n+5) . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 13 2008]
Triangle, with zeros omitted, given by (1, 0, -1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (0, 1, -1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - DELEHAM Philippe, Jan 16 2012
|
|
|
FORMULA
| Triangle read by rows, Pascal's triangle rows repeated.
Equals inverse binomial transform of A133156 unsigned.
G.f. : (1+x)/(1-(1+y)*x^2). - DELEHAM Philippe, Jan 16 2012
Sum_{k, 0<=k<=n} T(n,k)*x^k = A057077(n), A019590(n+1), A000012(n), A016116(n), A108411(n), A074872(n+1) for x = -2, -1, 0, 1, 2, 4 respectively. - DELEHAM Philippe, Jan 16 2012
|
|
|
EXAMPLE
| First few rows of the triangle =
1;
1;
1, 1;
1, 1;
1, 2, 1;
1, 2, 1;
1, 3, 3, 1;
1, 3, 3, 1;
1, 4, 6, 4, 1;
1, 4, 6, 4, 1;
1, 5, 10, 10, 5, 1;
1, 5, 10, 10, 5, 1;
...
Triangle (1,0,-1,0,0,...) DELTA (0,1,-1,0,0,...) begins :
1
1, 0
1, 1, 0
1, 1, 0, 0
1, 2, 1, 0, 0
1, 2, 1, 0, 0, 0
1, 3, 3, 1, 0, 0, 0
1, 3, 3, 1, 0, 0, 0, 0
1, 4, 6, 4, 1, 0, 0, 0, 0
1, 4, 6, 4, 1, 0, 0, 0, 0, 0
1, 5, 10, 10, 5, 1, 0, 0, 0, 0, 0...
|
|
|
CROSSREFS
| A007318, A133156, A051163
Sequence in context: A161107 A161042 A029292 * A159255 A035693 A068696
Adjacent sequences: A152195 A152196 A152197 * A152199 A152200 A152201
|
|
|
KEYWORD
| nonn,tabf
|
|
|
AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 28 2008
|
|
|
EXTENSIONS
| More terms from Philippe DELEHAM, Dec 14 2008
|
| |
|
|
