A161009 revision #6
|
|
A161009
|
|
Tribonacci left-bounded rhombic triangle.
|
|
1
|
|
|
1, 1, 1, 3, 2, 1, 7, 7, 3, 1, 18, 20, 12, 4, 1, 48, 59, 40, 18, 5, 1, 132, 174, 132, 68, 25, 6, 1, 372, 517, 426, 247, 105, 33, 7, 1, 1069, 1548, 1362, 864, 415, 152, 42, 8, 1, 3121, 4670, 4332, 2956, 1561, 648, 210, 52, 9, 1, 9232, 14188, 13746, 9960, 5685, 2604, 959, 280
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,4
|
|
REFERENCES
|
Sheng-Liang Yang et al., The Pascal rhombus and Riordan array, Fib. Q., 56:4 (2018), 337-347. See Fig. 3.
|
|
LINKS
|
|
|
FORMULA
|
Riordan array ((1/(1-x-x^2-x^2))*c((x/(1-x-x^2-x^3))^2),(x/(1-x-x^2-x^2))*c((x/(1-x-x^2-x^3))^2)).
T(n, m) = T'(n-1, m-1)+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.
|
|
EXAMPLE
|
Triangle begins
1,
1, 1,
3, 2, 1,
7, 7, 3, 1,
18, 20, 12, 4, 1,
48, 59, 40, 18, 5, 1,
132, 174, 132, 68, 25, 6, 1,
372, 517, 426, 247, 105, 33, 7, 1
We have, for instance, 132=59+18+40+12+3.
|
|
MAPLE
|
option remember;
if m < 0 or m >n then
0;
elif n = m then
1;
else
procname(n-1, m-1)+procname(n-1, m+1)+procname(n-1, m)+procname(n-2, m)+procname(n-3, m) ;
end if;
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|