OFFSET
1,5
COMMENTS
LINKS
E. Barcucci, R. Pinzani and R. Sprugnoli, Directed column-convex polyominoes by recurrence relations, Lecture Notes in Computer Science, No. 668, Springer, Berlin (1993), pp. 282-298.
FORMULA
G.f. of column k is f[k]-f[k-1], where f[k]=Sum(z^i, i=1..k)/[1-Sum(jz^j, j=1..k)] is the g.f. for directed column-convex polyominoes whose columns have height at most k.
EXAMPLE
Triangle starts:
1;
1,1;
1,3,1;
1,7,4,1;
1,15,12,5,1;
1,31,35,15,6,1;
MAPLE
f:=k->sum(z^i, i=1..k)/(1-sum(j*z^j, j=1..k)): T:=proc(n, k) if k<=n then coeff(series(f(k)-f(k-1), z=0, 15), z, n) else 0 fi end: for n from 1 to 12 do seq(T(n, k), k=1..n) od; # yields sequence in triangular form
MATHEMATICA
f[k_] := Sum[z^i, {i, 1, k}]/(1 - Sum[j*z^j, {j, 1, k}]);
T[n_, k_] := If[k <= n, SeriesCoefficient[f[k] - f[k-1], {z, 0, n}], 0];
Table[T[n, k], {n, 1, 12}, {k, 1, n}] // Flatten (* Jean-François Alcover, Aug 25 2024, after Maple program *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Emeric Deutsch, Aug 04 2006
STATUS
approved