A114096 Number of partitions of n into parts that are distinct mod 8.

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

Adjacent sequences: A114093 A114094 A114095 * A114097 A114098 A114099

Keyword

nonn

Author

Giovanni Resta, Feb 06 2006

Status

approved