|
| |
|
|
A104580
|
|
Tribonacci convolution triangle.
|
|
2
| |
|
|
1, 1, 1, 2, 2, 1, 4, 5, 3, 1, 7, 12, 9, 4, 1, 13, 26, 25, 14, 5, 1, 24, 56, 63, 44, 20, 6, 1, 44, 118, 153, 125, 70, 27, 7, 1, 81, 244, 359, 336, 220, 104, 35, 8, 1, 149, 499, 819, 864, 646, 357, 147, 44, 9, 1, 274, 1010, 1830, 2144, 1800, 1134, 546, 200, 54, 10, 1, 504
(list; table; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,4
|
|
|
COMMENTS
| First column is A000073(n+2). Row sums are A077939. Diagonal sums are A002478.
|
|
|
FORMULA
| Riordan array (1/(1-x-x^2-x^3), x/(1-x-x^2-x^3))
Contribution from Paul Barry (pbarry(AT)wit.ie), Jun 02 2009: (Start)
T(n, m) = T'(n-1, m-1)+T'(n-1, m)+T'(n-2, m)+T'(n-3,m), where T'(n, m) = T(n, m)
for n >= 0 and 0< = m< = n and T'(n, m) = 0 otherwise. (End)
T(n,k) = sum(binomial(i+k,k)trinomial(i,n-k-i),i=0..n-k), where trinomial(n,k) are the trinomial coefficients (A027907) [Emanuele Munarini, Mar 15 2011]
|
|
|
EXAMPLE
| Rows begin {1},{1,1},{2,2,1},{4,5,3,1},{7,12,9,4,1},...
|
|
|
PROG
| (Maxima) trinomial(n, k):=coeff(expand((1+x+x^2)^n), x, k);
create_list(sum(binomial(i+k, k)*trinomial(i, n-k-i), i, 0, n-k), n, 0, 8, k, 0, n); [Emanuele Munarini, Mar 15 2011]
|
|
|
CROSSREFS
| Sequence in context: A165038 A145036 A001404 * A202193 A105306 A183191
Adjacent sequences: A104577 A104578 A104579 * A104581 A104582 A104583
|
|
|
KEYWORD
| easy,nonn,tabl
|
|
|
AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Mar 16 2005
|
| |
|
|
