|
Search: id:A103284
|
|
|
| A103284 |
|
Triangle, read by rows, where row n+1 is formed by sorting, in ascending order, the result of the convolution of row n with {1,1}. |
|
+0
5
|
|
| 1, 1, 1, 1, 1, 2, 1, 2, 2, 3, 1, 3, 3, 4, 5, 1, 4, 5, 6, 7, 9, 1, 5, 9, 9, 11, 13, 16, 1, 6, 14, 16, 18, 20, 24, 29, 1, 7, 20, 29, 30, 34, 38, 44, 53, 1, 8, 27, 49, 53, 59, 64, 72, 82, 97, 1, 9, 35, 76, 97, 102, 112, 123, 136, 154, 179, 1, 10, 44, 111, 173, 179, 199, 214, 235, 259
(list; table; graph; listen)
|
|
|
OFFSET
|
0,6
|
|
|
COMMENT
|
Main diagonal is A103285.
|
|
EXAMPLE
|
Convolution of row 5 {1,4,5,6,7,9} with {1,1} = {1,5,9,11,13,16,9}; sort to obtain row 6: {1,5,9,9,11,13,16}.
Rows begin:
1,
1,1,
1,1,2,
1,2,2,3,
1,3,3,4,5,
1,4,5,6,7,9,
1,5,9,9,11,13,16,
1,6,14,16,18,20,24,29,
1,7,20,29,30,34,38,44,53,
1,8,27,49,53,59,64,72,82,97,
1,9,35,76,97,102,112,123,136,154,179,...
|
|
PROGRAM
|
(PARI) {T(n, k)=local(A=vector(n+1, i, vector(i)), B); A[1][1]=1; for(k=1, n, B=vector(k+1); B[1]=1; B[k+1]=A[k][k]; for(i=2, k, B[i]=A[k][i]+A[k][i-1]); A[k+1]=vecsort(B)); return(A[n+1][k+1])}
|
|
CROSSREFS
|
Cf. A103285.
Sequence in context: A033666 A139124 A024160 this_sequence A071287 A072084 A133755
Adjacent sequences: A103281 A103282 A103283 this_sequence A103285 A103286 A103287
|
|
KEYWORD
|
nonn,tabl
|
|
AUTHOR
|
Paul D. Hanna (pauldhanna(AT)juno.com), Jan 28 2005
|
|
|
Search completed in 0.002 seconds
|
