A353902 Number of partitions of n in which exactly one even part is repeated and odd parts are unrestricted.

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

Table of n, a(n) for n=1..50.

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

Cf. A000041, A353903.

Sequence in context: A068491 A364796 A239952 * A240076 A266771 A295342

Adjacent sequences: A353899 A353900 A353901 * A353903 A353904 A353905

Keyword

nonn

Author

Michel Marcus, May 10 2022

Status

approved