cp's OEIS Frontend

A069713 As a square array T(n,k) by antidiagonals, number of ways of partitioning k into up to n parts each no more than 5, or into up to 5 parts each no more than n; as a triangle t(n,k), number of ways of partitioning n into exactly k parts each no more than 6 (i.e., of arranging k indistinguishable standard dice to produce a total of n).

%I A069713 #6 Dec 01 2016 01:34:29
%S A069713 1,0,1,0,1,1,0,1,1,1,0,1,2,1,1,0,1,2,2,1,1,0,1,3,3,2,1,1,0,0,3,4,3,2,
%T A069713 1,1,0,0,3,5,5,3,2,1,1,0,0,2,6,6,5,3,2,1,1,0,0,2,6,8,7,5,3,2,1,1,0,0,
%U A069713 1,6,9,9,7,5,3,2,1,1,0,0,1,6,11,11,10,7,5,3,2,1,1,0,0,0,5,11,14,12,10,7,5
%N A069713 As a square array T(n,k) by antidiagonals, number of ways of partitioning k into up to n parts each no more than 5, or into up to 5 parts each no more than n; as a triangle t(n,k), number of ways of partitioning n into exactly k parts each no more than 6 (i.e., of arranging k indistinguishable standard dice to produce a total of n).
%F A069713 If k<6 T(n,k) = A068914(n,k). T(n,k) = T(n,5n-k); t(n,k) = t(7n-k,k). T(floor(5n/2),n) = t(n,floor(7n/2)) = A001975(n).
%e A069713 As square array, rows start: 1,0,0,0,0,0,...; 1,1,1,1,1,1,...; 1,1,2,2,3,3,...; 1,1,2,3,4,5,...; 1,1,2,3,5,6,...; 1,1,2,3,5,7,...; etc. As triangle, rows start: 1; 0,1; 0,1,1; 0,1,1,1; 0,1,2,1,1; 0,1,2,2,1,1; 0,1,3,3,2,1,1; etc. T(3,7)=6 since 7 can be written as 5+2, 5+1+1, 4+3, 4+2+1, 3+3+1, 3+2+2; or alternatively as 2+2+1+1+1, 3+1+1+1, 2+2+2+1, 3+2+1+1, 3+2+2, 3+3+1. t(10,3)=6 since 10 can be written as 6+3+1, 6+2+2, 5+4+1, 5+3+2, 4+4+2, 4+3+3.
%Y A069713 Cf. A061676 for a similar triangle, though with distinguishable dice (and a different offset). Antidiagonal sums of T(n, k), i.e., row sums (over k) of t(n, k), are A001402. First 22 terms are same as A068914 (see formula).
%K A069713 nonn,tabl
%O A069713 0,13
%A A069713 _Henry Bottomley_, Apr 01 2002