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A176084
Row sums of A175105.
1
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
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
KEYWORD
nonn
AUTHOR
Mats Granvik, Apr 08 2010
STATUS
approved