A117189 Binomial transform of the tribonacci sequence A000073 (shifted left twice).

1, 2, 5, 14, 40, 114, 324, 920, 2612, 7416, 21056, 59784, 169744, 481952, 1368400, 3885280, 11031424, 31321376, 88930368, 252498816, 716916544, 2035531648, 5779458048, 16409538688, 46591385856, 132286304768, 375598753024, 1066432564736, 3027907856384

Offset

0,2

Comments

a(n)/a(n-1) tends to 2.83928675... = A058265 + 1.

Partial sums are in A073357. - R. J. Mathar, Apr 02 2008

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-4,2).

Formula

Binomial transform of A000073 starting with A000073(2): (1, 1, 2, 4, 7, 13, ...).

a(n) = 4*a(n-1)-4*a(n-2)+2*a(n-3), n>2. - T. D. Noe, Nov 07 2006

O.g.f.: -(x-1)^2/(-1+4*x-4*x^2+2*x^3). - R. J. Mathar, Apr 02 2008

a(n) = 2*a(n-1) + Sum_{j=1..n-1} j*a(n-j-1), n>=1; with a(0) = 1. - Bob Selcoe, Jun 28 2014

Example

a(4) = 14 = 1*1 + 3*1 + 3*2 + 1*4;
a(6) = 324 = 2*114 + 1*40 + 2*14 + 3*5 + 4*2 + 5*1. - Bob Selcoe, Jun 28 2014

Mathematica

CoefficientList[Series[-(x - 1)^2/(-1 + 4*x - 4*x^2 + 2*x^3), {x, 0, 30}], x] (* Wesley Ivan Hurt, Jul 05 2014 *)
LinearRecurrence[{4, -4, 2}, {1, 2, 5}, 40] (* Harvey P. Dale, Oct 10 2016 *)

Crossrefs

Cf. A000073, A115390.

Sequence in context: A229737 A059505 A159035 * A052963 A329275 A036908

Adjacent sequences: A117186 A117187 A117188 * A117190 A117191 A117192

Keyword

nonn

Author

Gary W. Adamson, Mar 01 2006

Extensions

Corrected and extended by T. D. Noe, Nov 07 2006

Status

approved