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%I #6 Feb 22 2013 14:40:24
%S 1,1,1,2,4,2,5,13,11,3,13,40,46,24,5,34,120,172,128,50,8,89,354,603,
%T 572,319,98,13,233,1031,2025,2311,1651,733,187,21,610,2972,6592,8740,
%U 7548,4324,1600,348,34
%N Triangle T(n,k), read by rows, given by (1, 1, 1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 1, -1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.
%C T(n,n) = Fibonacci(n+1) = A000045(n+1).
%F 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) = T(1,0) = T(1,1) = 1 and T(n,k) = 0 if k<0 or if n<k.
%F G.f.: (1-2*x)/(1-(3+y)*x+(1-y^2)*x^2).
%F Sum_{k, 0<=k<=n} T(n,k)*x^k = A000007(n), A001519(n), A081294(n), A180036(n) for x = -1, 0, 1, 2 respectively.
%e Triangle begins :
%e 1
%e 1, 1
%e 2, 4, 2
%e 5, 13, 11, 3
%e 13, 40, 46, 24, 5
%e 34, 120, 172, 128, 50, 8
%e 89, 354, 603, 572, 319, 98, 13
%Y Cf. A000045, A001519, A123585, A202389, A202390,
%K nonn,tabl
%O 0,4
%A _Philippe Deléham_, Dec 18 2011
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