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A121062 Partition numbers mod 4.

%I A121062 #25 Dec 20 2024 12:27:24
%S A121062 1,1,2,3,1,3,3,3,2,2,2,0,1,1,3,0,3,1,1,2,3,0,2,3,3,2,0,2,2,1,0,2,1,3,
%T A121062 2,3,1,1,3,1,2,3,2,1,3,2,2,2,1,1,2,3,1,3,3,0,3,2,0,0,3,1,0,3,2,2,0,1,
%U A121062 3,1,0,1,3,1,0,0,3,3,0,2,0,3,3,1,0,1,2,1,1,1,1,3,3,1,0,3,0,2,0,3,0,2,3,2,1
%N A121062 Partition numbers mod 4.
%C A121062 P_n==0: 11, 15, 21, 26, 30, 55, 58, 59, 62, 66, 70, 74, 75, 78, 80, 84, 94, 96, 98, 100, ... A237278.
%C A121062 P_n==1: 0, 1, 4, 12, 13, 17, 18, 29, 32, 36, 37, 39, 43, 48, 49, 52, 61, 67, 69, 71, 73, ... A237279.
%C A121062 P_n==2: 2, 8, 9, 10, 19, 22, 25, 27, 28, 31, 34, 40, 42, 45, 46, 47, 50, 57, 64, 65, 79, ... A237280.
%C A121062 P_n==3: 3, 5, 6, 7, 14, 16, 20, 23, 24, 33, 35, 38, 41, 44, 51, 53, 54, 56, 60, 63, 68, ... A237281.
%H A121062 Alois P. Heinz, <a href="/A121062/b121062.txt">Table of n, a(n) for n = 0..10000</a>
%F A121062 a(n) = A000041(n) mod 4 = A010873(A000041(n)).
%F A121062 a(n) = A000025(n) mod 4. - _John M. Campbell_, Jun 29 2016
%p A121062 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A121062      (b(n, i-1)+b(n-i, min(n-i, i))) mod 4))
%p A121062     end:
%p A121062 a:= n-> b(n$2):
%p A121062 seq(a(n), n=0..104);  # _Alois P. Heinz_, Dec 20 2024
%t A121062 f[n_] := Mod[PartitionsP@n, 4]; Table[f@n, {n, 0, 104}] (* _Robert G. Wilson v_ *)
%o A121062 (PARI) a(n) = numbpart(n) % 4; \\ _Michel Marcus_, Jun 29 2016
%Y A121062 Cf. A000041, A010873, A049575.
%Y A121062 Cf. A237278, A237279, A237280, A237281.
%K A121062 nonn,easy
%O A121062 0,3
%A A121062 _Jonathan Vos Post_, Aug 10 2006
%E A121062 More terms from _Robert G. Wilson v_, Aug 17 2006