%I #6 Jan 09 2024 12:30:24
%S 1,8,1,27,12,1,64,40,14,1,125,96,49,16,1,216,187,117,55,17,1,343,324,
%T 228,133,60,18,1,512,514,396,259,145,64,19,1,729,768,628,450,284,155,
%U 67,20,1,1000,1093,938,713,493,304,164,70,20,1,1331,1500,1336
%N Rectangular array: R(n,k)=n^3+[(n^3)/2]+...+[(n^3)/k], where [ ]=floor, by antidiagonals.
%C For n>=1, row n is a homogeneous linear recurrence sequence with palindromic recurrence coefficients in the sense described at A211701.
%e Northwest corner:
%e 1...8....27...64....125...216...343
%e 1...12...40...96....187...324...514
%e 1...14...49...117...228...396...628
%e 1...16...55...133...259...450...713
%e 1...17...60...145...284...493...781
%e 1...18...64...155...304...529...838
%t f[n_, m_] := Sum[Floor[n^3/k], {k, 1, m}]
%t TableForm[Table[f[n, m], {m, 1, 40}, {n, 1, 16}]]
%t Flatten[Table[f[n + 1 - m, m], {n, 1, 14}, {m, 1, n}]]
%Y Cf. A211701
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Apr 20 2012