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 A381847 #35 Aug 04 2025 04:13:08
%S A381847 0,0,2,3,8,11,19,23,35,40,55,62,80,88,110,119,144,155,183,195,227,240,
%T A381847 275,290,328,344,386,403,448,467,515,535,587,608,663,686,744,768,830,
%U A381847 855,920,947,1015,1043,1115,1144,1219,1250,1328,1360,1442,1475,1560
%N A381847 a(n) is the number of ways to partition an n X n X n cube into 3 noncongruent cuboids.
%C A381847 Alternatively, a(n) is the number of ways to decompose the triplet (n,n,n) into 3 distinct unordered triplets.
%C A381847 Initial stage: One triplet of the form (n,n,n).
%C A381847 Second stage: Decompose the original triplet into two distinct triplets by splitting one of the elements of (x,y,z) into two parts at a time according to the following rule; (x,y,z) is replaced by (x,y,z-r), (x,y,r), where 0 < r <= z/2. Each resulting triplet must be distinct in element composition when comparing with the rest of the triplets in the set. Sets including the same element composition including the case r = z/2 are named as duplicates and set aside to reconsider when forming the next term.
%C A381847 Third stage: Apply the same rule to one of the two triplets of the second term at a time to create another two distinct triplets. At this stage consider the duplicates of the second term and apply the same rule to decompose one of the two identical triplets into two triplets of distinct element composition.
%H A381847 Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a381/A381847.java">Java program</a> (github)
%H A381847 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,1,-1,-2,0,1).
%F A381847 G.f.: x^3*(2+3*x+4*x^2+3*x^3+2*x^4)/((1+x+x^2)*(1+x)^2*(1-x)^3). - _Jinyuan Wang_, Aug 03 2025
%e A381847 (1,1,1) and (2,2,2) cannot be decomposed in three distinct triplets giving first two terms; a(1) = a(2) = 0.
%e A381847 (3,3,3) can be decomposed into two triplets (3,3,2), (3,3,1) by applying the rule and repeat the process for one the triplets at a time for obtaining the following two sets:
%e A381847 {(3,3,2), (3,2,1), (3,1,1)},
%e A381847 {(3,3,1), (3,2,2), (3,2,1)}.
%e A381847 Therefore, a(3) = 2.
%Y A381847 Cf. A384311, A384479, A385247.
%K A381847 nonn,easy
%O A381847 1,3
%A A381847 _Janaka Rodrigo_, May 06 2025
%E A381847 More terms from _Sean A. Irvine_, May 11 2025