|
|
A123262
|
|
Fibonacci-tribonacci triangle.
|
|
0
|
|
|
0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 3, 0, 0, 0, 0, 2, 5, 0, 0, 0, 0, 0, 5, 8, 0, 0, 0, 0, 0, 1, 10, 13, 0, 0, 0, 0, 0, 0, 3, 20, 21, 0, 0, 0, 0, 0, 0, 0, 9, 38, 34, 0, 0, 0, 0, 0, 0, 0, 1, 22, 71, 55, 0, 0, 0, 0, 0, 0, 0, 0, 4, 51, 130, 89, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 111, 235, 144
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,10
|
|
COMMENTS
|
Or, skew Jacobsthal-Lucas triangle, read by rows.
|
|
LINKS
|
|
|
FORMULA
|
T(n,k)=T(n-1,k-1)+T(n-2,k-2)+T(n-3,k-2), T(n,0)=0, T(1,1)=1, T(n,k)=0 if k<0 or if k>n . T(n,n)= Fibonacci(n)=A000045(n) . Sum_{k, 0<=k<=n}T(n,k)=A000073(n+1), tribonacci numbers . Sum_{n, n>=k}T(n,k)=A001045(k), Jacobsthal sequence.
|
|
EXAMPLE
|
Triangle begins:
.0;
.0, 1;
.0, 0, 1;
.0, 0, 0, 2;
.0, 0, 0, 1, 3;
.0, 0, 0, 0, 2, 5;
.0, 0, 0, 0, 0, 5, 8;
.0, 0, 0, 0, 0, 1, 10, 13;
.0, 0, 0, 0, 0, 0, 3, 20, 21;
.0, 0, 0, 0, 0, 0, 0, 9, 38, 34;
.0, 0, 0, 0, 0, 0, 0, 1, 22, 71, 55;
.0, 0, 0, 0, 0, 0, 0, 0, 4, 51, 130, 89;
.0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 111, 235, 144;
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|