A183202 Triangle, read by rows, where T(n,k) equals the sum of (n-k) terms in row n of triangle A131338 starting at position nk - k(k-1)/2, with the main diagonal formed from the row sums.

1, 1, 1, 2, 1, 2, 3, 3, 3, 5, 4, 6, 10, 9, 14, 5, 10, 22, 34, 29, 43, 6, 15, 40, 84, 122, 100, 143, 7, 21, 65, 169, 334, 463, 367, 510, 8, 28, 98, 300, 738, 1390, 1851, 1426, 1936, 9, 36, 140, 489, 1426, 3345, 6043, 7767, 5839, 7775, 10, 45, 192, 749, 2510, 6990, 15735

Offset

0,4

Links

Table of n, a(n) for n=0..61.

Example

Triangle begins:
1;
1,1;
2,1,2;
3,3,3,5;
4,6,10,9,14;
5,10,22,34,29,43;
6,15,40,84,122,100,143;
7,21,65,169,334,463,367,510;
8,28,98,300,738,1390,1851,1426,1936;
9,36,140,489,1426,3345,6043,7767,5839,7775;
10,45,192,749,2510,6990,15735,27374,34097,25094,32869; ...
The rows are derived from triangle A131338 by summing terms in the following manner:
(1);
(1),(1);
(1+1),(1),(2);
(1+1+1),(1+2),(3),(5);
(1+1+1+1),(1+2+3),(4+6),(9),(14);
(1+1+1+1+1),(1+2+3+4),(5+7+10),(14+20),(29),(43);
(1+1+1+1+1+1),(1+2+3+4+5),(6+8+11+15),(20+27+37),(51+71),(100),(143); ...
where row n of triangle A131338 consists of n '1's followed by the partial sums of the prior row.

Prog

(PARI) {A131338(n, k)=if(k>n*(n+1)/2|k<0, 0, if(k<=n, 1, sum(i=0, k-n, A131338(n-1, i))))}
{T(n, k)=if(n==k, A131338(n, n*(n+1)/2), sum(j=n*k-k*(k-1)/2, n*k-k*(k-1)/2+n-k-1, A131338(n, j)))}

Crossrefs

Cf. A131338, A098568, A098569 (row sums), A183203 (antidiagonal sums).

Sequence in context: A008681 A362559 A097242 * A306878 A161308 A161242

Adjacent sequences: A183199 A183200 A183201 * A183203 A183204 A183205

Keyword

tabl,nonn

Author

Paul D. Hanna, Dec 30 2010

Status

approved