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%I #5 Mar 30 2012 18:36:44
%S 1,1,1,1,3,1,2,6,5,1,3,11,15,7,1,4,20,36,28,9,1,6,35,78,85,45,11,1,9,
%T 59,159,221,166,66,13,1,13,98,309,522,509,287,91,15,1,19,161,579,1153,
%U 1382,1018,456,120,17,1,28,261,1056,2421,3444,3141,1840,681,153,19,1,41,419
%N Carrie's triangle, read by rows, where the terms are generated by the rule: T(n,k) = T(n-1,k) + T(n-1,k-1) + T(n-2,k-1) + T(n-3,k-1) + T(n-3,k), with T(0,0)=1.
%C Column 0 forms A000930. Row sums form A077938. This table was created by Carrie Hanna.
%F G.f.: A(x, y) = 1/(1-(1+y)*x-y*x^2-(1+y)*x^3).
%e Generated by adding preceding terms in the triangle
%e at positions that form the letter 'C': T(n,k) =
%e T(n-3,k-1) + T(n-3,k) +
%e T(n-2,k-1) +
%e T(n-1,k-1) + T(n-1,k).
%e Rows begin:
%e [1],
%e [1,1],
%e [1,3,1],
%e [2,6,5,1],
%e [3,11,15,7,1],
%e [4,20,36,28,9,1],
%e [6,35,78,85,45,11,1],
%e [9,59,159,221,166,66,13,1],
%e [13,98,309,522,509,287,91,15,1],
%e [19,161,579,1153,1382,1018,456,120,17,1],...
%o (PARI) {T(n,k)=if(n<k|k<0,0,if(n==0,1, T(n-1,k)+T(n-1,k-1)+T(n-2,k-1)+T(n-3,k-1)+T(n-3,k)))}
%Y Cf. A000930, A077938.
%K nonn,tabl
%O 0,5
%A _Paul D. Hanna_, Dec 24 2004
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