A211802 - OEIS

%I #21 Jul 06 2024 15:55:05

%S 0,3,0,11,3,0,28,13,3,0,56,32,13,3,0,99,64,34,13,3,0,159,113,68,34,13,

%T 3,0,240,181,117,70,34,13,3,0,344,272,187,125,70,34,13,3,0,475,388,

%U 282,197,125,70,34,13,3,0,635,535,406,292,203,125,70,34,13,3,0

%N R(k,n) = number of ordered triples (w,x,y) with all terms in {1,...,n} and 2*w^k < x^k + y^k; square array read by descending antidiagonals.

%C Row 1:  A182260.

%C Row 2:  A211800.

%C Row 3:  A211801.

%C Limiting row sequence: A016061.

%C Let R be the array in this sequence 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   0   3  11  28  56  99 159 240

%e   0   3  13  32  64 113 181 272

%e   0   3  13  34  68 117 187 282

%e   0   3  13  34  70 125 197 292

%e   0   3  13  34  70 125 203 302

%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}]  (* A182260 *)

%t Table[t[2, n], {n, 1, z}]  (* A211800 *)

%t Table[t[3, n], {n, 1, z}]  (* A211801 *)

%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}]] (* this sequence *)

%t Table[k (k - 1) (4 k + 1)/6, {k, 1,

%t   z}] (* row-limit sequence, A016061 *)

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

%Y Cf. A016061, A182260, A211790, A211800, A211801, A211802, A211805.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Apr 22 2012

%E Definition corrected by _Georg Fischer_, Sep 10 2022