OFFSET
0,5
COMMENTS
This triangle follows a general construction method as follows: Let a(n) be an integer sequence with a(0)=1, a(1)=1. Then T(n,k,r):=[k<=n](1+r*a(k)*a(n-k)) defines a symmetrical triangle.
Row sums are n + 1 + r*Sum_{k=0..n} a(k)*a(n-k) and central coefficients are 1+r*a(n)^2.
Here a(n)=1-0^n and r=1. Row sums are A004277.
Eigensequence of the triangle = A000129, the Pell sequence. - Gary W. Adamson, Feb 12 2009
Inverse has general element T(n,k)*(-1)^(n-k). - Paul Barry, Oct 06 2010
FORMULA
Number triangle T(n,k) = [k<=n](2-0^(n-k)-0^k+0^(n+k))=[k<=n](2-0^(k(n-k))).
a(n) = 2 - A103451(n). - Omar E. Pol, Jan 18 2009
EXAMPLE
Triangle begins
1;
1, 1;
1, 2, 1;
1, 2, 2, 1;
1, 2, 2, 2, 1;
1, 2, 2, 2, 2, 1;
1, 2, 2, 2, 2, 2, 1;
From Paul Barry, Oct 06 2010: (Start)
Production matrix is
1, 1;
0, 1, 1;
0, -1, 0, 1;
0, 1, 0, 0, 1;
0, -1, 0, 0, 0, 1;
0, 1, 0, 0, 0, 0, 1;
0, -1, 0, 0, 0, 0, 0, 1;
0, 1, 0, 0, 0, 0, 0, 0, 1; (End)
CROSSREFS
KEYWORD
AUTHOR
Paul Barry, Jan 07 2009
STATUS
approved