OFFSET
0,4
FORMULA
T(n,k) = A006456(n^2-k^2).
T(n,k) = [x^(n^2-k^2)] 1/(1 - Sum_{j>=1} x^(j^2)).
T(n,0) = Sum_{k=1..n} T(n,k) for n>=1.
EXAMPLE
Triangle begins:
1;
1, 1;
2, 1, 1;
11, 7, 3, 1;
124, 88, 30, 5, 1;
2870, 2024, 710, 124, 11, 1;
133462, 94137, 33033, 5767, 502, 22, 1;
12477207, 8800750, 3088365, 539192, 46832, 2024, 43, 1;
2344649612, 1653790807, 580347968, 101321507, 8800750, 380315, 8176, 88, 1;
885591183971, 624648802700, 219201637352, 38269865019, 3324109524, 143647802, 3088365, 33033, 175, 1; ...
where T(n,k) = coefficient of x^(n^2-k^2) in the series:
1/(1 - x - x^4 - x^9 - x^16 - x^25 - x^36 -...- x^(n^2) -...) = 1 + x + x^2 + x^3 + 2*x^4 + 3*x^5 + 4*x^6 + 5*x^7 + 7*x^8 + 11*x^9 + 16*x^10 + 22*x^11 + 30*x^12 + 43*x^13 + 62*x^14 + 88*x^15 + 124*x^16 + 175*x^17 + 249*x^18 + 354*x^19 + 502*x^20 + 710*x^21 + 1006*x^22 + 1427*x^23 + 2024*x^24 + 2870*x^25 +...
PROG
(PARI) {T(n, k)=polcoeff(1/(1-sum(m=1, n+1, x^(m^2))+x*O(x^(n^2-k^2))), n^2-k^2)}
for(n=0, 10, for(k=0, n, print1(T(n, k), ", ")); print(""))
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Paul D. Hanna, Nov 21 2013
STATUS
approved