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 A115127 #9 Aug 28 2019 16:57:43 %S A115127 3,6,7,10,16,19,15,30,47,56,21,50,95,146,174,28,77,170,311,471,561,36, %T A115127 112,280,586,1043,1562,1859,45,156,434,1015,2044,3564,5291,6292,55, %U A115127 210,642,1652,3682,7204,12363,18226,21658,66,275,915,2562,6230,13392,25623 %N A115127 Second (k=2) triangle of numbers related to totally asymmetric exclusion process (case alpha=1, beta=1). %C A115127 This is the second floor (k=2) of a pyramid of numbers, called X(1,1,k=2,n,m) with n>=m+1>=2. One could use offset n>=1 and add a zero main diagonal. %C A115127 The column sequences give for n>=m+1 and m=1..7: A000217, A005581, A024191, A115129, A115130, A115132, A115133. %C A115127 The diagonal sequences give for M:=n-m=1..3: A071716, A071726, A115134. %H A115127 W. Lang: <a href="/A115127/a115127.txt">First 10 rows.</a> %F A115127 a(n,m)= b(n,m) + b(n-1,m) with b(n,m):=A115126(n,m) if n=m+1 (main diagonal), A115126(n,m) + a(n,-1,m) if n>m+1 (subdiagonals) and 0 if n<m+1. %e A115127 [3];[6,7];[10,16,19];[15,30,47,56];... %e A115127 Main diagonal (n-m=1) example: a(3,2)= 7 = 5 + 2 because %e A115127 A115126(3,2)=5 and A115126(2,2)=2. %e A115127 Subdiagonal (n-m>1) example: a(4,2)= 16 = 9 + 7 because %e A115127 A115126(4,2)=9 and a(3,2)=7. %Y A115127 Row sums give A115128. %K A115127 nonn,easy,tabl %O A115127 2,1 %A A115127 _Wolfdieter Lang_, Jan 13 2006