cp's OEIS Frontend

A211783 Rectangular array: R(n,k)=n^2+[(n^2)/2]+...+[(n^2)/k], where [ ]=floor, by antidiagonals.

%I A211783 #7 Jan 09 2024 12:30:11
%S A211783 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 A211783 1,64,73,66,51,36,20,8,1,81,96,89,75,56,38,21,8,1,100,121,117,101,82,
%U A211783 60,40,22,8,1,121,150,148,133,110,88,63,42,23,8,1,144,181,183
%N A211783 Rectangular array:  R(n,k)=n^2+[(n^2)/2]+...+[(n^2)/k], where [ ]=floor, by antidiagonals.
%C A211783 For n>=1, row n is a homogeneous linear recurrence sequence with palindromic recurrence coefficients in the sense described at A211701.
%C A211783 Row 1:  A000290
%C A211783 Row 2:  A032528
%C A211783 Row 3:  A211784
%C A211783 R(n,n)=A118014(n,n)
%C A211783 The sequence approached as a limit of the rows is A175346: (1,8,23,50,87,140,...)
%e A211783 Northwest corner:
%e A211783 1....4....9....16....25....36
%e A211783 1....6....13...24....37....54
%e A211783 1....7....16...29....35....66
%e A211783 1....8....18...33....51....75
%e A211783 1....8....19...36....56....82
%e A211783 1....8....20...38....60....88
%e A211783 1....8....21...40....63....93
%t A211783 f[n_, m_] := Sum[Floor[n^2/k], {k, 1, m}]
%t A211783 TableForm[Table[f[n, m], {m, 1, 40}, {n, 1, 16}]]
%t A211783 Flatten[Table[f[n + 1 - m, m], {n, 1, 14}, {m, 1, n}]]
%Y A211783 Cf. A211701
%K A211783 nonn,tabl
%O A211783 0,2
%A A211783 _Clark Kimberling_, Apr 20 2012