A211805 - OEIS

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

%S 1,5,1,16,5,1,36,14,5,1,69,32,14,5,1,117,61,30,14,5,1,184,103,57,30,

%T 14,5,1,272,162,99,55,30,14,5,1,385,240,156,91,55,30,14,5,1,525,341,

%U 230,146,91,55,30,14,5,1,696,465,323,220,140,91,55,30,14,5,1,900

%N Rectangular array:  R(k,n) = number of ordered triples (w,x,y) with all terms in {1,...,n} and 2w^k>=x^k+y<k.

%C Row 1:  A055232

%C Row 2:  A211803

%C Row 3:  A211804

%C Limiting row sequence: A000330

%C Let R be the array in A211802 and let R' be the array in A211805.  Then R(k,n)+R'(k,n)=3^(n-1).

%C See the Comments at A211790.

%e Northwest corner:

%e 1...5...16...36...69...117...184

%e 1...5...14...32...61...103...162

%e 1...5...14...30...57...99....156

%e 1...5...14...30...55...91....146

%e 1...5...14...30...55...91....140

%t z = 48;

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

%t    (Do[If[2 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}]  (* A055232 *)

%t Table[t[2, n], {n, 1, z}]  (* A211803 *)

%t Table[t[3, n], {n, 1, z}]  (* A211804 *)

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

%t Flatten[Table[t[k, n - k + 1], {n, 1, 12},

%t                {k, 1, n}]] (* A211805 *)

%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 1,2

%A _Clark Kimberling_, Apr 22 2012