OFFSET
0,25
REFERENCES
J. Jordan and R. Southwell, Further Properties of Reproducing Graphs, Applied Mathematics, Vol. 1 No. 5, 2010, pp. 344-350. doi: 10.4236/am.2010.15045. - From N. J. A. Sloane, Feb 03 2013
LINKS
Alois P. Heinz, Rows n = 0..200, flattened
J. Jordan and R. Southwell, Further Properties of Reproducing Graphs, Applied Mathematics, Vol. 1 No. 5, 2010, pp. 344-350. doi: 10.4236/am.2010.15045. - From N. J. A. Sloane, Feb 03 2013
FORMULA
T(2m, k) = T(m, k)+T(2m-1, k-1); T(2m+1, k) = T(2m, k-1).
G.f.: 1/Product_{k>=0} (1-y*x^(2^k)). - Vladeta Jovovic, Dec 03 2003
EXAMPLE
1
0 1
0 1 1
0 0 1 1
0 1 1 1 1
0 0 1 1 1 1
0 0 1 2 1 1 1
0 0 0 1 2 1 1 1
0 1 1 1 2 2 1 1 1
0 0 1 1 1 2 2 1 1 1
0 0 1 2 2 2 2 2 1 1 1
0 0 0 1 2 2 2 2 2 1 1 1
MAPLE
A089052 := proc(n, k)
option remember;
if k > n then
return(0);
end if;
if k= 0 then
if n=0 then
return(1)
else
return(0);
end if;
end if;
if n mod 2 = 1 then
return procname(n-1, k-1);
end if;
procname(n-1, k-1)+procname(n/2, k);
end proc:
MATHEMATICA
t[n_, k_] := t[n, k] = Which[k > n, 0, k == 0, If[n == 0, 1, 0], Mod[n, 2] == 1, t[n-1, k-1], True, t[n-1, k-1] + t[n/2, k]]; Table[t[n, k], {n, 0, 13}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jan 14 2014, after Maple *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Dec 03 2003
STATUS
approved