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Rectangular array: R(n,k)=n^3+[(n^3)/2]+...+[(n^3)/k], where [ ]=floor, by antidiagonals.
1

%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