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%I #4 Mar 30 2012 18:36:32
%S 1,1,2,4,5,9,16,20,24,40,68,84,100,116,184,304,372,436,500,568,872,
%T 1412,1716,1988,2244,2516,2820,4232,6752,8164,9380,10468,11556,12772,
%U 14184,20936,33028
%N Triangle of numbers {a(n,k), n >= 0, 0<=k<=n} defined by a(0,0)=1, a(n+1,0)=A006319(n)=a(n,0) + Sum a(k,k), k=0..n-1. a(n,m+1)= a(n,0) + Sum A006319(k)*a(n-k-1,0), k=0..m-1.
%C Compare to A073150. Related to Royal paths in a lattice (A006318, A006319).
%F a(n, m+1) = a(n, 0) + Sum A006319(k)*a(n-k-1, 0), k=0..m-1.
%e a(4,2)=a(4,0)+1*a(3,0)+4*a(2,0)=68+(1*16+4*4)=100. a(4,0)=a(3,0)+a(3,3)+a(2,2)+a(1,1)+a(0,0)=16+(40+9+2+1)=68. Rows of triangle: {1}, {1,2}, {4,5,9}, {16,20,24,40}, {68,84,100,116,184},{304,372,436,500,568,872}, {1412,1716,1988,2244,2516,2820,4232}, ...
%Y Cf. A073150, A006319, A006318.
%K easy,nonn,tabl
%O 0,3
%A _Paul D. Hanna_, Jul 18 2002
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