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 A242110 Number of partitions of n whose different summands alternate in parity. 1
 1, 1, 2, 3, 4, 6, 8, 11, 13, 21, 23, 33, 39, 54, 63, 88, 98, 132, 157, 200, 237, 303, 356, 440, 526, 643, 767, 931, 1103, 1317, 1581, 1860, 2215, 2615, 3100, 3631, 4302, 4999, 5907, 6865, 8059, 9322, 10950, 12613, 14744, 16988, 19756, 22694, 26344, 30192 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS If the largest part is even (odd ), then the second largest part must be odd (even), the third largest part even (odd),... LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 Shane Chern, Unlimited parity alternating partitions, arXiv:1803.01031 [math.CO], 2018. EXAMPLE The first of the unrestricted partitions not to be counted is 3+1, because the largest part, 3, is odd and the next largest part, 1, is also odd. MAPLE b:= proc(n, i, t) option remember; `if`(n=0, 1, `if`(i<1, 0,       b(n, i-1, t) +`if`(irem(i+t, 2)=0, 0,       add(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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Last modified October 14 01:36 EDT 2019. Contains 327994 sequences. (Running on oeis4.)