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%I #18 Sep 11 2022 00:25:30
%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 diagonals.
%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}]] (* A211802 *)
%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
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