A211793 - OEIS

%I #28 Oct 28 2023 15:27:42

%S 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,

%T 80,53,30,14,5,1,0,120,121,88,55,30,14,5,1,0,165,175,134,90,55,30,14,

%U 5,1,0,220,244,195,138,91,55,30,14,5,1,0,286,327,270,201,139

%N 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.

%C Limiting row sequence: A000330.

%F A211790(k,n) + R(k,n) = 3^(n-1).

%e Northwest corner:

%e   0, 1, 4, 10, 20, 35, 56,  84

%e   0, 1, 5, 13, 28, 50, 80, 121

%e   0, 1, 5, 14, 29, 53, 88, 134

%e   0, 1, 5, 14, 30, 55, 90, 138

%e   0, 1, 5, 14, 30, 55, 91, 139

%e   0, 1, 5, 14, 30, 55, 91, 140

%t z = 48;

%t t[k_, n_] := Module[{s = 0},

%t    (Do[If[w^k >= x^k + y^k, s = s + 1],

%t        {w, 1, #}, {x, 1, #}, {y, 1, #}] &[n]; s)];

%t Table[t[1, n], {n, 1, z}]  (* A000292 *)

%t Table[t[2, n], {n, 1, z}]  (* A211636 *)

%t Table[t[3, n], {n, 1, z}]  (* A211651 *)

%t TableForm[Table[t[k, n], {k, 1, 12}, {n, 1, 16}]]

%t Flatten[Table[t[k, n - k + 1], {n, 1, 12}, {k, 1, n}]] (* this sequence *)

%t Table[k (k - 1) (2 k - 1)/6, {k, 1,

%t   z}] (* row-limit sequence, A000330 *)

%t (* _Peter J. C. Moses_, Apr 13 2012 *)

%Y Cf. A211790.

%Y Cf. A000292 (row 1), A211636 (row 2), A211651 (row 3), A000330.

%K nonn,tabl

%O 1,4

%A _Clark Kimberling_, Apr 21 2012