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Fibonacci-tribonacci triangle.
0

%I #6 Sep 08 2013 13:30:57

%S 0,0,1,0,0,1,0,0,0,2,0,0,0,1,3,0,0,0,0,2,5,0,0,0,0,0,5,8,0,0,0,0,0,1,

%T 10,13,0,0,0,0,0,0,3,20,21,0,0,0,0,0,0,0,9,38,34,0,0,0,0,0,0,0,1,22,

%U 71,55,0,0,0,0,0,0,0,0,4,51,130,89,0,0,0,0,0,0,0,0,0,14,111,235,144

%N Fibonacci-tribonacci triangle.

%C Or, skew Jacobsthal-Lucas triangle, read by rows.

%F T(n,k)=T(n-1,k-1)+T(n-2,k-2)+T(n-3,k-2), T(n,0)=0, T(1,1)=1, T(n,k)=0 if k<0 or if k>n . T(n,n)= Fibonacci(n)=A000045(n) . Sum_{k, 0<=k<=n}T(n,k)=A000073(n+1), tribonacci numbers . Sum_{n, n>=k}T(n,k)=A001045(k), Jacobsthal sequence.

%e Triangle begins:

%e .0;

%e .0, 1;

%e .0, 0, 1;

%e .0, 0, 0, 2;

%e .0, 0, 0, 1, 3;

%e .0, 0, 0, 0, 2, 5;

%e .0, 0, 0, 0, 0, 5, 8;

%e .0, 0, 0, 0, 0, 1, 10, 13;

%e .0, 0, 0, 0, 0, 0, 3, 20, 21;

%e .0, 0, 0, 0, 0, 0, 0, 9, 38, 34;

%e .0, 0, 0, 0, 0, 0, 0, 1, 22, 71, 55;

%e .0, 0, 0, 0, 0, 0, 0, 0, 4, 51, 130, 89;

%e .0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 111, 235, 144;

%Y Cf. A037027.

%K nonn,tabl

%O 0,10

%A _Philippe Deléham_, Nov 06 2006