cp's OEIS Frontend

A227272 T(n,k,r) is the total number of parts in the set of partitions of an n X k X r rectangular cuboid into integer-sided cubes, considering only the list of parts; irregular triangle T(n,k,r), n >= k >= r >= 1, read by rows.

%I A227272 #22 Sep 06 2021 04:25:08
%S A227272 1,2,4,9,3,6,17,9,29,48,4,8,27,12,51,97,16,90,192,363,5,10,39,15,69,
%T A227272 145,20,130,311,685,25,180,459,1056
%N A227272 T(n,k,r) is the total number of parts in the set of partitions of an n X k X r rectangular cuboid into integer-sided cubes, considering only the list of parts; irregular triangle T(n,k,r), n >= k >= r >= 1, read by rows.
%H A227272 Christopher Hunt Gribble, <a href="/A227272/a227272.cpp.txt">C++ program</a>
%F A227272 T(n,k,1) = n*k.
%F A227272 T(n,2,2) = (n+1)(n+2) - 3.
%e A227272 The irregular triangle begins:
%e A227272 .   r   1    2    3    4 ...
%e A227272 n,k
%e A227272 1,1     1
%e A227272 2,1     2
%e A227272 2,2     4    9
%e A227272 3,1     3
%e A227272 3,2     6   17
%e A227272 3,3     9   29   48
%e A227272 4,1     4
%e A227272 4,2     8   27
%e A227272 4,3    12   51   97
%e A227272 4,4    16   90  192  363
%e A227272 5,1     5
%e A227272 5,2    10   39
%e A227272 5,3    15   69  145
%e A227272 5,4    20  130  311  685
%e A227272 5,5    25  180  459 1056 ...
%e A227272 ...
%e A227272 T(2,2,2) = 9 because a 2 X 2 X 2 rectangular cuboid has 2 partitions, (8 1 X 1 X 1 squares) and (1 2 X 2 X 2 square) with 9 parts in total.
%Y A227272 Cf. A225622.
%K A227272 nonn,tabf
%O A227272 1,2
%A A227272 _Christopher Hunt Gribble_, Sep 02 2013