This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A077228 #7 Mar 30 2012 18:51:39 %S A077228 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 A077228 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 A077228 1,4,27,190,432,462,330,165,55,11,1,1,4,27,221,687,918,792,495,220,66 %N A077228 Triangle of compositions with a total that is no more than n into exactly k parts each no more than k. %H A077228 <a href="/index/Com#comp">Index entries for sequences related to compositions</a> %F A077228 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 A077228 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 A077228 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 A077228 nonn,tabl %O A077228 0,5 %A A077228 _Henry Bottomley_, Oct 30 2002