|
| |
|
|
A051631
|
|
Triangle formed using Pascal's rule except begin and end n-th row with n-1.
|
|
3
| |
|
|
-1, 0, 0, 1, 0, 1, 2, 1, 1, 2, 3, 3, 2, 3, 3, 4, 6, 5, 5, 6, 4, 5, 10, 11, 10, 11, 10, 5, 6, 15, 21, 21, 21, 21, 15, 6, 7, 21, 36, 42, 42, 42, 36, 21, 7, 8, 28, 57, 78, 84, 84, 78, 57, 28, 8, 9, 36, 85, 135, 162, 168, 162, 135, 85, 36, 9
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,7
|
|
|
COMMENTS
| Row sums give A000918(n).
Central terms for n>0: T(2*n,n)=A024483(n+1), T(n,[n/2])=A116385(n-1); for n>1: T(n,1) = T(n,n-1) = A000217(n-2). [Reinhard Zumkeller, Nov 13 2011]
|
|
|
LINKS
| Reinhard Zumkeller, Rows n=0..100 of triangle, flattened
Index entries for triangles and arrays related to Pascal's triangle
|
|
|
FORMULA
| T(n,k) = T(n-1,k) + T(n-1,k-1), 0 < k < n, T(n,0) = T(n,n) = n - 1.
|
|
|
EXAMPLE
| -1;
0, 0;
1, 0, 1;
2, 1, 1, 2;
3, 3, 2, 3, 3;
4, 6, 5, 5, 6, 4; ...
|
|
|
PROG
| (Haskell)
a051631 n k = a051631_tabl !! n !! k
a051631_row n = a051631_tabl !! n
a051631_list = concat a051631_tabl
a051631_tabl = iterate (\row -> zipWith (+) ([1] ++ row) (row ++[1])) [-1]
-- Reinhard Zumkeller, Nov 13 2011
|
|
|
CROSSREFS
| Cf. A007318.
Sequence in context: A156267 A160325 A054989 * A073725 A055223 A174807
Adjacent sequences: A051628 A051629 A051630 * A051632 A051633 A051634
|
|
|
KEYWORD
| easy,nice,sign
|
|
|
AUTHOR
| Asher Auel (asher.auel(AT)reed.edu)
|
|
|
EXTENSIONS
| Definition modified and keyword tabl added by Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 13 2011
|
| |
|
|
