A176084 Row sums of A175105.

1, 2, 4, 9, 22, 58, 160, 454, 1311, 3828, 11260, 33290, 98778, 293866, 875960, 2614891, 7814544, 23373354, 69955372, 209478678, 627521578, 1880400340, 5636065932, 16895989570, 50658893073

Offset

1,2

Comments

a(n+1)/a(n) tends to 3.

a(n)/A007051(n) tends to Product_{k>=1} (1-1/((3^k + 1)/2)). To observe the asymptote one needs 1000 or more decimal digits of the constant c=Product_{k>=1} (1-1/((3^k + 1)/2)). - Mats Granvik, Jan 02 2015

Links

Table of n, a(n) for n=1..25.

Formula

a(n) ~ Product_{k>=1} (1-1/((3^k + 1)/2))*A007051(n). - Mats Granvik, Jan 01 2015

Example

a(25)/A007051(24) = 50658893073/141214768241 = 0.35873650967258963431... which is close to 0.35792312728995990302591...

Mathematica

Clear[t]; nn = 25; t[n_, 1] = 1; t[n_, k_] := t[n, k] = If[n >= k, Sum[t[n - i, k - 1], {i, 1, k - 1}] + Sum[t[n - i, k], {i, 1, k - 1}], 0]; Table[Sum[t[n, k], {k, 1, n}], {n, 1, nn}](* Mats Granvik, Jan 02 2015 *)

Crossrefs

Cf. A177510.

Sequence in context: A337067 A249563 A124380 * A192576 A059019 A249560

Adjacent sequences: A176081 A176082 A176083 * A176085 A176086 A176087

Keyword

nonn

Author

Mats Granvik, Apr 08 2010

Status

approved