Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #7 Jan 09 2024 12:30:11
%S 1,4,1,9,6,1,16,13,7,1,25,24,16,8,1,36,37,29,18,8,1,49,54,45,33,19,8,
%T 1,64,73,66,51,36,20,8,1,81,96,89,75,56,38,21,8,1,100,121,117,101,82,
%U 60,40,22,8,1,121,150,148,133,110,88,63,42,23,8,1,144,181,183
%N Rectangular array: R(n,k)=n^2+[(n^2)/2]+...+[(n^2)/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.
%C Row 1: A000290
%C Row 2: A032528
%C Row 3: A211784
%C R(n,n)=A118014(n,n)
%C The sequence approached as a limit of the rows is A175346: (1,8,23,50,87,140,...)
%e Northwest corner:
%e 1....4....9....16....25....36
%e 1....6....13...24....37....54
%e 1....7....16...29....35....66
%e 1....8....18...33....51....75
%e 1....8....19...36....56....82
%e 1....8....20...38....60....88
%e 1....8....21...40....63....93
%t f[n_, m_] := Sum[Floor[n^2/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 0,2
%A _Clark Kimberling_, Apr 20 2012