W. Lang Oct 10 2008 A145363 tabf array: partition numbers M31hat(-2). Partitions of n listed in Abramowitz-Stegun order p. 831-2 (see the main page for an A-number with the reference). n\k 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 ... 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 2 4 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 4 2 4 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 4 0 4 8 2 4 2 1 0 0 0 0 0 0 0 0 0 0 0 7 0 0 0 0 0 0 4 8 0 4 8 2 4 2 1 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 8 0 0 4 8 16 0 4 8 2 4 2 1 . . . . n\k 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 ... The next two rows, for n=9 and n=10, are: n=9: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, 16, 0, 0, 4, 8, 16, 0, 4, 8, 2, 4, 2, 1], n=10: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 16, 0, 0, 0, 0, 8, 16, 32, 0, 0, 4, 8, 16, 0, 4, 8, 2, 4, 2, 1]. The row sums give, for n>=1, A145365: [1,3,5,9,13,25,33,57,81,129,...]. They coincide with the row sums of triangle A145364 = S1hat(-2). ########################################### e.o.f. #####################################################################################