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

Author

N. J. A. Sloane, Sep 16 2009

Keywords

• nonn
• easy

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)

Programs

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 *)

Extensions

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