|
| |
|
|
A131268
|
|
Triangle read by rows: T(n,k)=2* binomial(n-floor((k+1)/2),floor(k/2))-1 (0<=k<=n).
|
|
2
| |
|
|
1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 5, 3, 1, 1, 1, 7, 5, 5, 1, 1, 1, 9, 7, 11, 5, 1, 1, 1, 11, 9, 19, 11, 7, 1, 1, 1, 13, 11, 29, 19, 19, 7, 1, 1, 1, 15, 13, 41, 29, 39, 19, 9, 1, 1, 1, 17, 15, 55, 41, 69, 39, 29, 9, 1, 1, 1, 19, 17, 71, 55, 111, 69, 69, 29, 11, 1, 1, 1, 21, 19, 89, 71, 167
(list; table; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,9
|
|
|
COMMENTS
| Row sums = A131269: (1, 2, 3, 6, 11, 20, 35,...). Reversal = triangle A131270.
|
|
|
FORMULA
| 2*A065941 - A000012, where A065941 = Pascal's triangle with repeated columns; and A000012 = (1; 1,1; 1,1,1;...) as an infinite lower triangular matrix.
|
|
|
EXAMPLE
| First few rows of the triangle are:
1;
1, 1;
1, 1, 1;
1, 1, 3, 1;
1, 1, 5, 3, 1;
1, 1, 7, 5, 5, 1;
1, 1, 9, 7, 11, 5, 1;
1, 1, 11, 9, 19, 11, 7, 1;
...
|
|
|
MAPLE
| T := proc (n, k) options operator, arrow; 2*binomial(n-floor((1/2)*k+1/2), floor((1/2)*k))-1 end proc: for n from 0 to 12 do seq(T(n, k), k = 0 .. n) end do; # yields sequence in triangular form - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 15 2007
|
|
|
CROSSREFS
| Cf. A065941, A000012, A131269, A131270.
Sequence in context: A028234 A052125 A081060 * A109221 A046643 A112475
Adjacent sequences: A131265 A131266 A131267 * A131269 A131270 A131271
|
|
|
KEYWORD
| nonn,tabl
|
|
|
AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 23 2007
|
|
|
EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 15 2007
|
| |
|
|
