A048516 - OEIS

A048516

Array T read by diagonals: T(m,n)=number of subsets S of {1,2,3,...,m+n-1} such that |S|>1 and |a-b|>=m for all distinct a and b in S, m=1,2,3,...; n=1,2,3,...

%I #8 Jun 19 2021 22:30:23

%S 0,0,1,0,4,1,0,11,3,1,0,26,7,3,1,0,57,14,6,3,1,0,120,26,11,6,3,1,0,

%T 247,46,19,10,6,3,1,0,502,79,31,16,10,6,3,1,0,1013,133,49,25,15,10,6,

%U 3,1,0,2036,221,76,38,22,15,10,6,3,1,0,4083,364

%N Array T read by diagonals: T(m,n)=number of subsets S of {1,2,3,...,m+n-1} such that |S|>1 and |a-b|>=m for all distinct a and b in S, m=1,2,3,...; n=1,2,3,...

%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a048/A048516.java">Java program</a> (github)

%F T(m,n) = [x^m] 1/((1-x^2)*(1-x-x^n)). - _Sean A. Irvine_, Jun 19 2021

%e Diagonals: {0}; {1,0}; {4,1,0}; ...

%Y A000295 (row 1), A001924 (row 2), A050228 (row 3).

%K nonn,tabl

%O 1,5

%A _Clark Kimberling_