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%I #7 Mar 30 2012 18:51:39
%S 1,1,1,1,3,1,1,4,4,1,1,4,10,5,1,1,4,17,15,6,1,1,4,23,35,21,7,1,1,4,26,
%T 66,56,28,8,1,1,4,27,106,126,84,36,9,1,1,4,27,150,247,210,120,45,10,1,
%U 1,4,27,190,432,462,330,165,55,11,1,1,4,27,221,687,918,792,495,220,66
%N Triangle of compositions with a total that is no more than n into exactly k parts each no more than k.
%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%F T(n, k) =a(n-1, k)+A077227(n, k). If n>=k^2, T(n, k)=n^n. If k<=n<2k, T(n, k)=C(n, k).
%e Rows start: 1; 1,1; 1,3,1; 1,4,4,1; 1,4,10,5,1; 1,4,17,15,6,1; 1,4,23,35,21,7,1; etc. T(6,3)=17 since compositions with 3 parts each no more than 3 and a total no more than 6 are: 1+1+1, 1+1+2, 1+1+3, 1+2+1, 1+2+2, 1+2+3, 1+3+1, 1+3+2, 2+1+1, 2+1+2, 2+1+3, 2+2+1, 2+2+2, 2+3+1, 3+1+1, 3+1+2 and 3+2+1.
%Y Rows eventually start like A000312. Central diagonal is A001700. Right hand side and central diagonal is like right hand side of A007318. Cf. A077227.
%K nonn,tabl
%O 0,5
%A _Henry Bottomley_, Oct 30 2002