A211799 - OEIS

%I #5 Dec 04 2016 19:46:28

%S 0,0,0,1,1,0,4,5,1,0,10,13,5,1,0,20,26,14,5,1,0,35,48,29,14,5,1,0,56,

%T 78,53,30,14,5,1,0,84,119,88,55,30,14,5,1,0,120,173,134,90,55,30,14,5,

%U 1,0,165,240,195,138,91,55,30,14,5,1,0,220,323,270,201,139,91

%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 Row 1:  A002292

%C Row 2:  A211637

%C Row 3:  A211651

%C Limiting row sequence: A000330

%C Let R be the array in A211796 and let R' be the array in A211799.  Then R(k,n)+R'(k,n)=3^(n-1).

%C See the Comments at A211790.

%e Northwest corner:

%e 0...0...1...4....10...20...35...56

%e 0...1...5...13...26...48...78...119

%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

%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}]  (* A211637 *)

%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],

%t     {n, 1, 12}, {k, 1, n}]] (* A211799 *)

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

%t     {k, 1, z}] (* row-limit sequence, A000330 *)

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

%Y Cf. A211790.

%K nonn,tabl

%O 1,7

%A _Clark Kimberling_, Apr 21 2012