OFFSET
0,2
COMMENTS
T(n,n) = Fibonacci(n+2) = A000045(n+2).
FORMULA
T(n,k) = 3*T(n-1,k) + T(n-1,k-1) + T(n-2,k-2) - T(n-2,k) with T(0,0) = 1, T(1,0) = T(1,1) = 2 and T(n,k) = 0 if k<0 or if n<k.
G.f.: (1+(y-1)*x)/(1-(3+y)*x+(1-y^2)*x^2).
Sum_{k, 0<=k<=n} T(n,k)*x^k = A000007(n), A122367(n), A000302(n), A180035(n) for x = -1, 0, 1, 2 respectively.
Sum_{k, 0<=k<=n} T(n,k)*3^k = 2^n * A055099(n). - Philippe Deléham, Feb 05 2012
EXAMPLE
Triangle begins :
1
2, 2
5, 8, 3
13, 27, 19, 5
34, 86, 86, 42, 8
89, 265, 338, 234, 85, 13
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Philippe Deléham, Dec 18 2011
STATUS
approved