A353903 Number of partitions of n in which exactly one odd part is repeated and even parts are unrestricted.

0, 1, 1, 2, 3, 6, 8, 11, 16, 24, 32, 43, 58, 79, 103, 132, 172, 225, 285, 359, 455, 575, 716, 886, 1099, 1361, 1669, 2036, 2486, 3032, 3669, 4422, 5334, 6420, 7687, 9178, 10951, 13045, 15481, 18321, 21669, 25593, 30129, 35394, 41549, 48700, 56941, 66456, 77491, 90242

Offset

1,4

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), nbor=0, vp=Vec(p)); for (i=1, #s, if (((s[i] % 2) == 1) && (#select(x->(x==s[i]), vp) > 1), nbor++); ); if (nbor == 1, nbp++); ); nbp; }

Crossrefs

Cf. A000041, A353902.

Sequence in context: A211519 A329384 A342493 * A325547 A242340 A033766

Adjacent sequences: A353900 A353901 A353902 * A353904 A353905 A353906

Keyword

nonn

Author

Michel Marcus, May 10 2022

Status

approved