|
| |
|
|
A051601
|
|
Rows of triangle formed using Pascal's rule except we begin and end the n-th row with n.
|
|
1
| |
|
|
0, 1, 1, 2, 2, 2, 3, 4, 4, 3, 4, 7, 8, 7, 4, 5, 11, 15, 15, 11, 5, 6, 16, 26, 30, 26, 16, 6, 7, 22, 42, 56, 56, 42, 22, 7, 8, 29, 64, 98, 112, 98, 64, 29, 8, 9, 37, 93, 162, 210, 210, 162, 93, 37, 9, 10, 46, 130, 255, 372, 420, 372, 255, 130, 46
(list; table; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,4
|
|
|
COMMENTS
| The number of spotlight tilings of an m-by-n rectangle missing the southeast corner. E.g. there are 2 spotlight tilings of a 2 X 2 square missing its southeast corner. - Bridget Eileen Tenner (bridget(AT)math.depaul.edu), Nov 10 2007
|
|
|
REFERENCES
| B. E. Tenner, <a href="http://dx.doi.org/10.1007/s00026-011-0077-6">Spotlight tiling</a>, Ann. Combinat. 14 (4) (2010) 553-568.
|
|
|
FORMULA
| T(m,n) = binomial(m+n,m) - 2*binomial(m+n-2,m-1), up to offset and transformation of array to triangular indices. - Bridget Eileen Tenner (bridget(AT)math.depaul.edu), Nov 10 2007
t(n,k)= Binomial[n, k + 1] + Binomial[n, n - k + 1]. [From Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 17 2009]
|
|
|
EXAMPLE
| Contribution from Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 17 2009: (Start)
0;
1, 1;
2, 2, 2;
3, 4, 4, 3;
4, 7, 8, 7, 4;
5, 11, 15, 15, 11, 5;
6, 16, 26, 30, 26, 16, 6;
7, 22, 42, 56, 56, 42, 22, 7;
8, 29, 64, 98, 112, 98, 64, 29, 8;
9, 37, 93, 162, 210, 210, 162, 93, 37, 9;
10, 46, 130, 255, 372, 420, 372, 255, 130, 46, 10;
11, 56, 176, 385, 627, 792, 792, 627, 385, 176, 56, 11;
12, 67, 232, 561, 1012, 1419, 1584, 1419, 1012, 561, 232, 67, 12; (End)
|
|
|
MATHEMATICA
| Contribution from Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 17 2009: (Start)
t[n_, k_] = Binomial[n, k + 1] + Binomial[n, n - k + 1];
Table[Table[t[n, k], {k, 0, n}], {n, 0, 12}];
Flatten[%] (End)
|
|
|
CROSSREFS
| Row sums give A000918(n+1).
Sequence in context: A096009 A000224 A085201 * A193921 A074829 A060243
Adjacent sequences: A051598 A051599 A051600 * A051602 A051603 A051604
|
|
|
KEYWORD
| easy,nonn,tabl
|
|
|
AUTHOR
| Asher Auel (asher.auel(AT)reed.edu)
|
| |
|
|
