OFFSET
1,4
COMMENTS
Limiting row sequence: A000330.
FORMULA
A211790(k,n) + R(k,n) = 3^(n-1).
EXAMPLE
Northwest corner:
0, 1, 4, 10, 20, 35, 56, 84
0, 1, 5, 13, 28, 50, 80, 121
0, 1, 5, 14, 29, 53, 88, 134
0, 1, 5, 14, 30, 55, 90, 138
0, 1, 5, 14, 30, 55, 91, 139
0, 1, 5, 14, 30, 55, 91, 140
MATHEMATICA
z = 48;
t[k_, n_] := Module[{s = 0},
(Do[If[w^k >= x^k + y^k, s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}] &[n]; s)];
Table[t[1, n], {n, 1, z}] (* A000292 *)
Table[t[2, n], {n, 1, z}] (* A211636 *)
Table[t[3, n], {n, 1, z}] (* A211651 *)
TableForm[Table[t[k, n], {k, 1, 12}, {n, 1, 16}]]
Flatten[Table[t[k, n - k + 1], {n, 1, 12}, {k, 1, n}]] (* this sequence *)
Table[k (k - 1) (2 k - 1)/6, {k, 1,
z}] (* row-limit sequence, A000330 *)
(* Peter J. C. Moses, Apr 13 2012 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Apr 21 2012
STATUS
approved