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A114096
Number of partitions of n into parts that are distinct mod 8.
2
1, 1, 2, 2, 3, 4, 5, 6, 8, 9, 12, 13, 16, 20, 23, 26, 31, 37, 42, 47, 54, 65, 72, 80, 90, 108, 115, 129, 145, 168, 184, 200, 220, 259, 270, 301, 336, 375, 411, 436, 477, 546, 568, 631, 700, 755, 832, 862, 945, 1050
OFFSET
1,3
LINKS
Fausto A. C. Cariboni, Table of n, a(n) for n = 1..800
EXAMPLE
a(7)=5 because there are 5 such partition of 7: {7}, {1,6}, {2,5}, {3,4}, {4,2,1}.
MATHEMATICA
<< DiscreteMath`Combinatorica`; np[n_]:= Length@Select[Mod[ #, 8]& /@ Partitions[n], (Length@# != Length@Union@#)&]; lst = Array[np, 50]
Table[Count[IntegerPartitions[n], _?(Max[Tally[Mod[#, 8]][[All, 2]]]==1&)], {n, 50}] (* Harvey P. Dale, Apr 17 2021 *)
CROSSREFS
Sequence in context: A340751 A319069 A029013 * A008582 A069911 A185225
KEYWORD
nonn
AUTHOR
Giovanni Resta, Feb 06 2006
STATUS
approved