

A211785


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


1



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
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OFFSET

1,2


COMMENTS

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


LINKS

Table of n, a(n) for n=1..58.


EXAMPLE

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


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}]]


CROSSREFS

Cf. A211701
Sequence in context: A002173 A050458 A125166 * A075155 A075151 A028943
Adjacent sequences: A211782 A211783 A211784 * A211786 A211787 A211788


KEYWORD

nonn,tabl


AUTHOR

Clark Kimberling, Apr 20 2012


STATUS

approved



