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A211793
Rectangular array: R(k,n) = number of ordered triples (w,x,y) with all terms in {1,...,n} and w^k >= x^k + y^k.
1
0, 1, 0, 4, 1, 0, 10, 5, 1, 0, 20, 13, 5, 1, 0, 35, 28, 14, 5, 1, 0, 56, 50, 29, 14, 5, 1, 0, 84, 80, 53, 30, 14, 5, 1, 0, 120, 121, 88, 55, 30, 14, 5, 1, 0, 165, 175, 134, 90, 55, 30, 14, 5, 1, 0, 220, 244, 195, 138, 91, 55, 30, 14, 5, 1, 0, 286, 327, 270, 201, 139
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
Cf. A211790.
Cf. A000292 (row 1), A211636 (row 2), A211651 (row 3), A000330.
Sequence in context: A089962 A363971 A127155 * A145880 A048516 A060638
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Apr 21 2012
STATUS
approved