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

Author

Gary W. Adamson, Mar 01 2006

Keywords

• nonn

Comments

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

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

Examples

			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
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-4,2).

Crossrefs

Cf. A000073, A115390.

Programs

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 *)

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

Extensions

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