|
%I #6 Feb 19 2014 12:03:14
%S 1,0,2,0,1,2,0,0,3,2,0,0,1,5,2,0,0,0,4,7,2,0,0,0,1,9,9,2,0,0,0,0,5,16,
%T 11,2,0,0,0,0,1,14,25,13,2,0,0,0,0,0,6,30,36,15,2,0,0,0,0,0,1,20,55,
%U 49,17,2,0,0,0,0,0,0,7,50,91,64,19,2,0,0,0,0,0
%N A skewed version of triangular array A029653.
%C Triangle T(n,k), 0<=k<=n, read by rows, given by (0, 1/2, -1/2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (2, -1, 0, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.
%C Row sums are Fib(n+2).
%C Column sums are A003945(k).
%C Diagonal sums are (-1)^(n+1)*A109266(n+1).
%C T(3*n,2*n) = A029651(n).
%F G.f.: (1+x*y)/(1-x*y-x^2*y).
%F T(n,k) = T(n-1,k-1) + T(n-2,k-1), T(0,0) = 1, T(1,0) = 0, T(1,1) = 2, T(n,k) = 0 if k<0 or if k>n.
%F Sum_{k=0..n} T(n,k)*x^k = A000007(n), A000045(n+2), A026150(n+1), A108306(n), A164545(n), A188168(n+1) for x = 0, 1, 2, 3, 4, 5 respectively.
%e Triangle begins:
%e 1;
%e 0, 2;
%e 0, 1, 2;
%e 0, 0, 3, 2;
%e 0, 0, 1, 5, 2;
%e 0, 0, 0, 4, 7, 2;
%e 0, 0, 0, 1, 9, 9, 2;
%e 0, 0, 0, 0, 5, 16, 11, 2;
%e 0, 0, 0, 0, 1, 14, 25, 13, 2;
%e 0, 0, 0, 0, 0, 6, 30, 36, 15, 2;
%e 0, 0, 0, 0, 0, 1, 20, 55, 49, 17, 2;
%e 0, 0, 0, 0, 0, 0, 7, 50, 91, 64, 19, 2;
%e ...
%Y Cf. A029635, A029653, A178524.
%K easy,nonn,tabl
%O 0,3
%A _Philippe Deléham_, Feb 18 2014
|
