A114095 Number of partitions of n into parts that are distinct mod 7.

1, 1, 2, 2, 3, 4, 5, 6, 7, 10, 10, 13, 16, 18, 21, 24, 31, 31, 38, 44, 49, 56, 62, 76, 76, 90, 100, 113, 126, 136, 161, 161, 186, 201, 234, 252, 267, 308, 308, 349, 370, 449, 462, 483, 546, 546, 609, 637, 813, 792

Offset: 1

Author

Giovanni Resta, Feb 06 2006

Keywords

• nonn

Examples

			a(7)=5 because there are 5 such partitions of 7: {7}, {1,6}, {2,5}, {3,4}, {4,2,1}.
		

Links

• Fausto A. C. Cariboni, Table of n, a(n) for n = 1..1000

Programs

Mathematica

<< DiscreteMath`Combinatorica`; np[n_]:= Length@Select[Mod[ #,7]& /@ Partitions[n],(Length@# == Length@Union@#)&]; lst = Array[np,50] (* corrected by Seth A. Troisi, May 17 2022 *)

PARI

a(n) = my(nb=0); forpart(p=n, if (#p == #Set(apply(x->(x%7), Vec(p))), nb++)); nb; \\ Michel Marcus, May 18 2022