OFFSET
1,3
COMMENTS
FORMULA
G.f.=sum(t^k*x^(k(3k-1)/2)*(1+x^(2k))*product((1+x^j)/(1-x^j), j=1..k-1)/(1-x^k), k=1..infinity).
EXAMPLE
T(8,2)=4 because we have [6,2], [5,3], [5,2,1] and [4,3,1].
Triangle starts:
1;
1;
2;
2;
2,1;
2,2;
2,3;
2,4;
MAPLE
g:=sum(t^k*x^(k*(3*k-1)/2)*(1+x^(2*k))*product((1+x^j)/(1-x^j), j=1..k-1)/(1-x^k), k=1..10): gser:=simplify(series(g, x=0, 36)): for n from 1 to 32 do P[n]:=sort(coeff(gser, x^n)) od: for n from 1 to 32 do seq(coeff(P[n], t^j), j=1..floor((1+sqrt(1+24*n))/6)) od; # yields sequence in triangular form
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
_Emeric Deutsch_, Feb 26 2006
STATUS
approved