%I #45 Jun 14 2020 12:57:17
%S 0,0,0,1,1,3,5,7,9,12,15,19,23,28,35,43,47,52,61,67,76,85,94,105,114,
%T 125,137,149,161,175,190,203,216,232,246,261,278,292,309,329,346,365,
%U 384,404,426,449,470,493,516,536,562,587,611,637,665,691,719,746,770,800,831,860,889,923,951,983
%N Number of integers from 0 to the triangular number A000217(n) that cannot be represented as a difference of triangular numbers from 0 to n.
%F a(n) = A000217(n) - A334821(n) + 1.
%e a(2) = 0 as all four numbers from 0 to A000217(2) = 3 can be represented as a difference of 0,1,3, the triangular numbers from 0 to 2.
%e a(3) = 1 as in the seven numbers from 0 to A000217(3) = 6, one number, 4, cannot be represented as a difference of 0,1,3,6, the triangular numbers from 0 to 3. The other five numbers can be.
%e a(6) = 5 as in the twenty-two numbers from 0 to A000217(6) = 21, five numbers, 8,13,16,17,19, cannot be represented as a difference of 0,1,3,6,10,15,21, the triangular numbers from 0 to 6. The other seventeen numbers can be.
%Y Cf. A334821, A234813, A000217, A001227.
%K nonn
%O 0,6
%A _Scott R. Shannon_, Jun 09 2020