A123326 Let M be the matrix defined in A111490. Sequence gives the sum of the elements of the submatrices (from the upper left element): M(1,1); M(1,1)+M(1,2)+M(1,2)+M(2,2); M(1,1)+M(1,2)+M(1,3)+M(2,1)+M(2,2)+M(2,3)+M(3,1)+M(3,2)+M(3,3), etc.
1, 5, 13, 27, 47, 77, 114, 165, 226, 302, 391, 502, 622, 768, 933, 1120, 1325, 1564, 1819, 2112, 2424, 2768, 3143, 3564, 3998, 4477, 4993, 5551, 6138, 6783, 7447, 8173, 8933, 9745, 10606, 11525, 12462, 13473, 14539, 15667, 16826, 18067, 19339, 20697, 22104
Offset: 1
Examples
a(4) = 1+1+1+1 + 1+2+1+2 + 1+2+3+1 + 1+2+3+4 = 27.
Formula
a(n) = Sum_{i=1..n} Sum_{j=1..n} M(i,j).
a(n) = a(n-1) + A121896(n) with a(0)=0.