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A353902
Number of partitions of n in which exactly one even part is repeated and odd parts are unrestricted.
1
0, 0, 0, 1, 1, 2, 3, 6, 8, 13, 18, 26, 36, 51, 68, 93, 123, 164, 214, 278, 358, 461, 586, 744, 937, 1177, 1468, 1826, 2260, 2788, 3425, 4195, 5118, 6228, 7552, 9135, 11016, 13252, 15899, 19031, 22724, 27075, 32188, 38189, 45214, 53431, 63020, 74200, 87205, 102318
OFFSET
1,6
LINKS
George E. Andrews and Mircea Merca, On the Number of Even Parts in All Partitions of n into Distinct Parts, Ann. Comb. 24, 47-54 (2020).
Nyirenda Darlison and Mugwangwavari Beaullah, Extentions and variations of Andrews-Merca identities, arXiv:2205.03697 [math.CO], 2022. See p. 7 ff.
Shishuo Fu and Dazhao Tang, Generalizing a partition theorem of Andrews, arXiv:1705.05046 [math.CO], 2017.
PROG
(PARI) a(n) = {my(nbp=0); forpart(p=n, my(s=Set(p), nber=0, vp=Vec(p)); for (i=1, #s, if (((s[i] % 2) == 0) && (#select(x->(x==s[i]), vp) > 1), nber++); ); if (nber == 1, nbp++); ); nbp; }
CROSSREFS
Sequence in context: A068491 A364796 A239952 * A240076 A266771 A295342
KEYWORD
nonn
AUTHOR
Michel Marcus, May 10 2022
STATUS
approved