OFFSET
0,5
COMMENTS
The second diagonal, T(n,n-1) = A003095(n). - Cortney Reagle, Sep 17 2019
LINKS
Cortney Reagle, Table of n, a(n) for n = 0..104 (Rows n = 0..12 of the triangle, flattened)
FORMULA
T(n, k) = T(n-1, k-1)^2 + T(n-1, k)^2; T(0,0) = 1; T(n,-1) = 0; T(n, k) = 0, n < k.
EXAMPLE
Triangle T(n,k) (with rows n >= 0 and columns 0 <= k <= n) begins as follows:
1;
1, 1;
1, 2, 1;
1, 5, 5, 1;
1, 26, 50, 26, 1;
1, 677, 3176, 3176, 677, 1;
1, 458330, 10545305, 20173952, 10545305, 458330, 1;
...
PROG
(PARI) T(n)={my(M=matrix(n, n)); M[1, 1]=1; for(n=2, n, M[n, 1]=1; for(k=2, n, M[n, k]=M[n-1, k-1]^2 + M[n-1, k]^2)); M}
{ my(A=T(7)); for(i=1, #A, print(A[i, 1..i])) } \\ Andrew Howroyd, Sep 17 2019
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Philippe Deléham, Jun 09 2006
EXTENSIONS
a(12) = 50 inserted and more terms added by Cortney Reagle, Sep 17 2019
STATUS
approved