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

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, 1, 64, 73, 66, 51, 36, 20, 8, 1, 81, 96, 89, 75, 56, 38, 21, 8, 1, 100, 121, 117, 101, 82, 60, 40, 22, 8, 1, 121, 150, 148, 133, 110, 88, 63, 42, 23, 8, 1, 144, 181, 183

Offset: 0

Author

Clark Kimberling, Apr 20 2012

Keywords

• nonn
• tabl

Comments

For n>=1, row n is a homogeneous linear recurrence sequence with palindromic recurrence coefficients in the sense described at A211701.

Row 1: A000290

Row 2: A032528

Row 3: A211784

R(n,n)=A118014(n,n)

The sequence approached as a limit of the rows is A175346: (1,8,23,50,87,140,...)

Examples

			Northwest corner:
1....4....9....16....25....36
1....6....13...24....37....54
1....7....16...29....35....66
1....8....18...33....51....75
1....8....19...36....56....82
1....8....20...38....60....88
1....8....21...40....63....93
		

Crossrefs

Cf. A211701

Programs

Mathematica

f[n_, m_] := Sum[Floor[n^2/k], {k, 1, m}]
TableForm[Table[f[n, m], {m, 1, 40}, {n, 1, 16}]]
Flatten[Table[f[n + 1 - m, m], {n, 1, 14}, {m, 1, n}]]