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A117189 Binomial transform of the tribonacci sequence A000073 (shifted left twice). 5
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 (list; graph; refs; listen; history; text; internal format)
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) = 4a(n-1)-4a(n-2)+2a(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

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Last modified September 18 23:17 EDT 2020. Contains 337175 sequences. (Running on oeis4.)