OFFSET
1,3
COMMENTS
LINKS
E. Barcucci, A. Del Lungo, R. Pinzani and R. Sprugnoli, La hauteur des polyominos dirigés verticalement convexes, Séminaire Lotharingien de Combinatoire, B31d (1993), 11 pp.
FORMULA
G.f. G(t,z) satisfies G(t,z)=zt(1-t)/(1-t-2zt+zt^2) +z(z-1)t^2*G(t,tz)/[(1-t-2zt+zt^2)(1-zt)]
EXAMPLE
Triangle starts:
1;
0,2,1;
0,0,4,5,3,1;
0,0,0,8,15,17,15,9,4,1;
0,0,0,0,16,39,59,75,78,67,48,29,14,5,1;
MAPLE
A:=t*z*(1-t)/(1-t-2*t*z+t^2*z): B:=t^2*z*(z-1)/((1-t-2*t*z+t^2*z)*(1-t*z)): Aser:=simplify(series(A, z=0, 12)): Bser:=simplify(series(B, z=0, 12)): for n to 12 do A[n]:=coeff(Aser, z, n): B[n]:=coeff(Bser, z, n) end do: P[1]:=A[1]: for n from 2 to 7 do P[n]:=sort(expand(simplify(A[n]+add(B[n-j]*P[j]*t^j, j=1..n-1)))) end do: for n to 7 do seq(coeff(P[n], t, j), j=1..(1/2)*n*(n+1)) end do;
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Emeric Deutsch, Jan 21 2008
STATUS
approved