W. Lang, Okt 10 2007 a(n,m) tabl head (triangle) for A008284, =p(n,m) number of m parts partititons of n. n\m 1 2 3 4 5 6 7 8 9 10 ... 1 1 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 3 1 1 1 0 0 0 0 0 0 0 4 1 2 1 1 0 0 0 0 0 0 5 1 2 2 1 1 0 0 0 0 0 6 1 3 3 2 1 1 0 0 0 0 7 1 3 4 3 2 1 1 0 0 0 8 1 4 5 5 3 2 1 1 0 0 9 1 4 7 6 5 3 2 1 1 0 10 1 5 8 9 7 5 3 2 1 1 . . . The row sums give p(n)=A000041(n), the numbers of partitions of n: [1, 2, 3, 5, 7, 11, 15, 22, 30, 42, ...]. The alternating row sums give [1, 0, 1, -1, 1, -1, 1, -2, 2, -2, 2, -3, 3, -3, 4, -5, 5, -5, 6, -7, 8, -8, 9, -11, 12,...]. Number of odd part partitions minus number of even part partitions of n. The negative of A081362(n). Unsigned this looks like A000700(n). ################################## e.o.f. ############################