OFFSET
2,6
COMMENTS
LINKS
Alois P. Heinz, Rows n = 2..200, flattened
FORMULA
G.f.: 1/(1 - t*Sum_{i>=1} z^prime(i)).
EXAMPLE
T(9,3) = 4 because we have [2,2,5], [2,5,2], [5,2,2] and [3,3,3].
Triangle starts:
1;
1;
0, 1;
1, 2;
0, 1, 1;
1, 2, 3;
0, 2, 3, 1;
0, 2, 4, 4;
...
MAPLE
G:=1/(1-t*sum(z^ithprime(i), i=1..30))-1: Gser:=simplify(series(G, z=0, 25)): for n from 2 to 21 do P[n]:=sort(coeff(Gser, z, n)) od: for n from 2 to 21 do seq(coeff(P[n], t, j), j=1..floor(n/2)) od; # yields sequence in triangular form
# second Maple program:
with(numtheory):
b:= proc(n) option remember; local j; if n=0 then [1]
else []; for j to pi(n) do zip((x, y)->x+y, %,
[0, b(n-ithprime(j))[]], 0) od; % fi
end:
T:= n-> subsop(1=NULL, b(n))[]:
seq(T(n), n=2..20); # Alois P. Heinz, May 23 2013
MATHEMATICA
nn=20; a[x_]:=Sum[x^Prime[n], {n, 1, nn}]; CoefficientList[Series[1/(1-y a[x]), {x, 0, nn}], {x, y}]//Grid (* Geoffrey Critzer, Nov 08 2013 *)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Emeric Deutsch, Aug 06 2006
STATUS
approved