This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A071335 #24 Mar 28 2023 12:37:34
%S A071335 0,1,1,1,2,2,3,2,3,3,3,3,4,3,4,4,5,4,5,4,6,5,6,6,6,6,7,5,8,5,8,5,10,6,
%T A071335 8,8,10,6,11,5,12,7,12,7,13,7,14,9,13,9,15,7,17,8,15,8,17,7,17,10,18,
%U A071335 9,20,8,21,11,21,8,21,7,23,11,23,11,23,10,28,12,25,11,26
%N A071335 Number of partitions of n into sum of at most three primes.
%C A071335 a(n) = A010051(n) + A061358(n) + A068307(n). [From _Reinhard Zumkeller_, Aug 08 2009]
%H A071335 T. D. Noe, <a href="/A071335/b071335.txt">Table of n, a(n) for n=1..10000</a>
%e A071335 a(21)=6 as 21 = 2+19 = 2+2+17 = 3+5+13 = 3+7+11 = 5+5+11 = 7+7+7.
%t A071335 goldbachcount[p1_] := (parts=IntegerPartitions[p1, 3]; count=0; n=1;
%t A071335 While[n<=Length[parts], If[Intersection[Flatten[PrimeQ[parts[[n]]]]][[1]]==True, count++]; n++]; count); Table[goldbachcount[i], {i, 1, 100}] (* _Frank M Jackson_, Mar 25 2013 *)
%t A071335 Table[Length[Select[IntegerPartitions[n,3],AllTrue[#,PrimeQ]&]],{n,90}] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Oct 21 2016 *)
%Y A071335 Cf. A002375, A068307, A025583.
%K A071335 nonn,look
%O A071335 1,5
%A A071335 _Reinhard Zumkeller_, May 19 2002