OFFSET
1,2
LINKS
Alois P. Heinz, Rows n = 1..26, flattened
EXAMPLE
T(8,4) = 3: {1,6}, {2,5}, {3,4}, {7} have element sum 7, {1,7}, {2,6}, {3,5}, {8} have element sum 8, and {1,8}, {2,7}, {3,6}, {4,5} have element sum 9.
Triangle begins:
. 1;
. 3;
. 7, 1;
. 15, 3;
. 31, 7, 1;
. 63, 17, 3;
. 127, 43, 8, 1;
. 255, 108, 22, 3;
MAPLE
b:= proc(l, n, k) option remember; local i, j; `if`(l=[0$k], 1, `if`(add(j, j=l)>n*(n-1)/2, 0, b(l, n-1, k))+ add(`if`(l[j] -n<0, 0, b(sort([seq(l[i] -`if`(i=j, n, 0), i=1..k)]), n-1, k)), j=1..k)) end: T:= (n, k)-> add(b([t$k], n, k), t=2*k-1..floor(n*(n+1)/(2*k)))/k!:
seq(seq(T(n, k), k=1..ceil(n/2)), n=1..15);
MATHEMATICA
b[l_List, n_, k_] := b[l, n, k] = Module[{i, j}, If[l == Array[0&, k], 1, If [Total[l] > n*(n-1)/2, 0, b[l, n-1, k]] + Sum [If [l[[j]] - n < 0, 0, b[Sort[Table[l[[i]] - If[i == j, n, 0], {i, 1, k}]], n-1, k]], {j, 1, k}]] ]; T[n_, k_] := Sum[b[Array[t&, k], n, k], {t, 2*k-1, Floor[n*(n+1)/(2*k)]}]/k!; Table[Table[T[n, k], {k, 1, Ceiling[n/2]}], {n, 1, 15}] // Flatten (* Jean-François Alcover, Dec 17 2013, translated from Maple *)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Alois P. Heinz, Sep 29 2011
STATUS
approved