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 A242984 Number of partitions of n where the frequencies alternate in parity. 1
 1, 1, 2, 2, 4, 4, 6, 7, 11, 12, 15, 19, 26, 30, 37, 42, 58, 64, 82, 92, 120, 129, 167, 181, 241, 252, 326, 346, 450, 474, 606, 641, 822, 863, 1088, 1146, 1454, 1526, 1898, 2010, 2494, 2638, 3232, 3437, 4195, 4458, 5381, 5748, 6928, 7389, 8805, 9446, 11217 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Let the frequency of the largest summand be f1, the frequency of the next smaller summand be f2, etc. Then the sequence f1, f2, f3, ... alternates in parity. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 EXAMPLE For example the partition 3,2,2,1 is counted since the frequency of 3 is 1; the frequency of 2 is 2; and the frequency of 1 is 1. So the sequence of frequencies is 1,2,1. Since the terms of this sequence are odd, even, odd this partition is counted. MAPLE b:= proc(n, i, t) option remember; `if`(n=0, 1, `if`(i<1, 0,       b(n, i-1, t) +add(`if`(irem(j+t, 2)=0, 0,       b(n-i*j, i-1, 1-t)), j=1..n/i)))     end: a:= n-> `if`(n=0, 1, add(b(n\$2, j), j=0..1)): seq(a(n), n=0..80);  # Alois P. Heinz, Aug 17 2014 MATHEMATICA <

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