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%I #5 Dec 04 2016 19:46:28
%S 1,5,1,16,5,1,36,16,5,1,69,36,16,5,1,117,69,38,16,5,1,184,119,73,38,
%T 16,5,1,272,190,123,75,38,16,5,1,385,282,194,131,75,38,16,5,1,525,399,
%U 290,204,131,75,38,16,5,1,696,547,415,300,210,131,75,38,16,5,1
%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: A211806
%C Row 3: A211807
%C Limiting row sequence: A000330
%C Let R be the array in A211808 and let R' be the array in A182259. 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...16...36...69...119...190
%e 1...5...16...38...73...123...194
%e 1...5...16...38...75...131...204
%e 1...5...16...38...75...131...210
%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}] (* A211806 *)
%t Table[t[3, n], {n, 1, z}] (* A211807 *)
%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}]] (* A211808 *)
%t Table[k (4 k^2 - 3 k + 5)/6,
%t {k, 1, z}] (* row-limit sequence, A174723 *)
%t (* _Peter J. C. Moses_, Apr 13 2012 *)
%Y Cf. A211790.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Apr 22 2012
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