OFFSET
1,2
LINKS
Alois P. Heinz, Rows n = 1..141, flattened (Rows n = 1..21 from Christopher Hunt Gribble)
Christopher Hunt Gribble, C++ program
FORMULA
Sum_{k=1..n} T(n,k) * k^2 = A037444(n) * n^2.
EXAMPLE
For n = 3, the 4 partitions are:
Square side 1 2 3
9 0 0
5 1 0
1 2 0
0 0 1
Total 15 3 1
So T(3,1) = 15, T(3,2) = 3, T(3,3) = 1.
The triangle begins:
.\ k 1 2 3 4 5 6 7 8 9 ...
.n
.1 1
.2 4 1
.3 15 3 1
.4 50 11 2 1
.5 156 35 10 4 1
.6 460 101 36 14 4 1
.7 1296 298 105 44 16 6 1
.8 3522 798 300 130 56 23 6 1
.9 9255 2154 827 377 174 82 31 9 1
10 23672 5490 2164 1015 502 243 108 43 10 ...
11 59050 13914 5525 2658 1350 705 343 154 55 ...
MAPLE
b:= proc(n, i) option remember;
`if`(n=0 or i=1, 1+n*x, b(n, i-1)+
`if`(i^2>n, 0, (g->g+coeff(g, x, 0)*x^i)(b(n-i^2, i))))
end:
T:= n-> (p->seq(coeff(p, x, i), i=1..n))(b(n^2, n)):
seq(T(n), n=1..14); # Alois P. Heinz, Sep 24 2013
MATHEMATICA
b[n_, i_] := b[n, i] = If[n==0 || i==1, 1+n*x, b[n, i-1] + If[i^2>n, 0, Function[ {g}, g+Coefficient[g, x, 0]*x^i][b[n-i^2, i]]]]; T[n_] := Function[{p}, Table[ Coefficient[p, x, i], {i, 1, n}]][ b[n^2, n]]; Table[T[n], {n, 1, 14}] // Flatten (* Jean-François Alcover, Mar 09 2015, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Christopher Hunt Gribble, Sep 24 2013
STATUS
approved