OFFSET
1,2
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1799 (rows 1..200)
Eric Weisstein's World of Mathematics, Durfee Square
EXAMPLE
Triangle begins:
1;
3;
6;
10, 2;
15, 5;
21, 14;
28, 26;
36, 50;
45, 80, 3;
PROG
(PARI) \\ by enumeration over partitions.
ds(p)={for(i=2, #p, if(p[#p+1-i]<i, return(i-1))); #p}
row(n)={my(v=vector(sqrtint(n))); forpart(p=n, v[ds(p)] += #p); v}
{ for(n=1, 10, print(row(n))) } \\ Andrew Howroyd, Feb 02 2022
(PARI) \\ by generating function.
P(n, k, y)={1/prod(j=1, k, 1 - y*x^j + O(x*x^n))}
T(n, k)={my(r=n-k^2); if(r<0, 0, subst(deriv(polcoef(y^k*P(r, k, 1)*P(r, k, y), r)), y, 1))}
{ for(n=1, 10, print(vector(sqrtint(n), k, T(n, k)))) } \\ Andrew Howroyd, Feb 02 2022
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Omar E. Pol, Dec 22 2019
EXTENSIONS
Terms a(10) and beyond from Andrew Howroyd, Feb 02 2022
STATUS
approved