A211785 Rectangular array: R(n,k)=n^3+[(n^3)/2]+...+[(n^3)/k], where [ ]=floor, by antidiagonals.

1, 8, 1, 27, 12, 1, 64, 40, 14, 1, 125, 96, 49, 16, 1, 216, 187, 117, 55, 17, 1, 343, 324, 228, 133, 60, 18, 1, 512, 514, 396, 259, 145, 64, 19, 1, 729, 768, 628, 450, 284, 155, 67, 20, 1, 1000, 1093, 938, 713, 493, 304, 164, 70, 20, 1, 1331, 1500, 1336

Offset: 1

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.

Examples

			Northwest corner:
1...8....27...64....125...216...343
1...12...40...96....187...324...514
1...14...49...117...228...396...628
1...16...55...133...259...450...713
1...17...60...145...284...493...781
1...18...64...155...304...529...838
		

Crossrefs

Cf. A211701

Programs

Mathematica

f[n_, m_] := Sum[Floor[n^3/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}]]