|
Search: id:A115085
|
|
|
| A115085 |
|
Triangle, read by rows, where T(n,k) equals the dot product of the vector of terms in row n-1 from T(n-1,k) to T(n-1,n-1) with the vector of terms in column k+1 from T(k+1,k+1) to T(n,k+1): T(n,k) = Sum_{j=0..n-k-1} T(n-1,j+k)*T(j+k+1,k+1) for n>k+1>0, with T(n,n) = 1 and T(n,n-1) = n (n>=1). |
|
+0
6
|
|
| 1, 1, 1, 3, 2, 1, 12, 5, 3, 1, 58, 21, 7, 4, 1, 321, 102, 32, 9, 5, 1, 1963, 579, 158, 45, 11, 6, 1, 13053, 3601, 933, 226, 60, 13, 7, 1, 92946, 24426, 5939, 1395, 306, 77, 15, 8, 1, 702864, 176858, 41385, 9097, 1977, 398, 96, 17, 9, 1, 5599204, 1359906, 306070
(list; table; graph; listen)
|
|
|
OFFSET
|
0,4
|
|
|
COMMENT
|
Triangle A115080 is the dual of this triangle.
|
|
EXAMPLE
|
T(n,k)=[T(n-1,k),T(n-1,k+1),..,T(n-1,n-1)]*[T(k+1,k+1),T(k+2,k+1),..,T(n,k+1)]:
12 = [3,2,1]*[1,2,5] = 3*1 + 2*2 + 1*5;
21 = [5,3,1]*[1,3,7] = 5*1 + 3*3 + 1*7;
102 = [21,7,4,1]*[1,3,7,32] = 21*1 + 7*3 + 4*7 + 1*32;
158 = [32,9,5,1]*[1,4,9,45] = 32*1 + 9*4 + 5*9 + 1*45.
Triangle begins:
1;
1,1;
3,2,1;
12,5,3,1;
58,21,7,4,1;
321,102,32,9,5,1;
1963,579,158,45,11,6,1;
13053,3601,933,226,60,13,7,1;
92946,24426,5939,1395,306,77,15,8,1;
702864,176858,41385,9097,1977,398,96,17,9,1;
5599204,1359906,306070,65310,13195,2691,502,117,19,10,1; ...
|
|
PROGRAM
|
(PARI) {T(n, k)=if(n==k, 1, if(n==k+1, n, sum(j=0, n-k-1, T(n-1, j+k)*T(j+k+1, k+1))))}
|
|
CROSSREFS
|
Cf. A115086 (column 0), A115087 (column 1), A115088 (column 2), A115089 (row sums); A115080 (dual triangle).
Sequence in context: A123513 A117442 A118435 this_sequence A110616 A059418 A092582
Adjacent sequences: A115082 A115083 A115084 this_sequence A115086 A115087 A115088
|
|
KEYWORD
|
nonn,tabl
|
|
AUTHOR
|
Paul D. Hanna (pauldhanna(AT)juno.com), Jan 13 2006
|
|
|
Search completed in 0.002 seconds
|
