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A353903
Number of partitions of n in which exactly one odd part is repeated and even parts are unrestricted.
1
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
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
Sequence in context: A211519 A329384 A342493 * A325547 A242340 A033766
KEYWORD
nonn
AUTHOR
Michel Marcus, May 10 2022
STATUS
approved