A152074 Rows sums of triangle A152072.

1, 3, 6, 11, 18, 30, 46, 73, 111, 170, 254, 392, 574, 868, 1294, 1933, 2834, 4267, 6228, 9312, 13674, 20162, 29528, 44132, 63945, 94390, 138562, 203706, 296436, 438976, 635776, 936263, 1367034, 1997200, 2907862, 4290047, 6192784, 9070744, 13248374

Offset

1,2

Comments

From David W. Wilson, Jul 07 2016: (Start)

Empirically, it appears that

lim n->inf a(n+3)/a(n) = 3.

lim n->inf a(3n+1)/a(3n) = 312/217.

lim n->inf a(3n+2)/a(3n+1) = 75/52.

lim n->inf a(3n+3)/a(3n+2) = 217/150. (End)

References

David W. Wilson, Posting to Sequence Fans mailing List, Mar 11 2009

Links

David W. Wilson and Vaclav Kotesovec, Table of n, a(n) for n = 1..2000 (first 1000 terms from David W. Wilson)

Maple

A152072 := proc(n, k) mul(floor((n+i)/k), i=0..k-1) ; end: A152074 := proc(n) add( A152072(n, k), k=1..n) ; end: seq(A152074(n), n=1..80) ; # R. J. Mathar, Sep 18 2009

Mathematica

Table[Total@ Map[Product[Floor[(n + i)/#], {i, 0, # - 1}] &, Range@ n], {n, 40}] (* Michael De Vlieger, Jul 09 2016, after Robert G. Wilson v at A152072 *)

Crossrefs

Sequence in context: A265075 A147079 A281572 * A123629 A212484 A279100

Adjacent sequences: A152071 A152072 A152073 * A152075 A152076 A152077

Keyword

nonn,easy

Author

N. J. A. Sloane, Sep 16 2009

Extensions

More terms from R. J. Mathar, Sep 18 2009

Status

approved