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A132308 2*3^n - n - 1. 2
1, 4, 15, 50, 157, 480, 1451, 4366, 13113, 39356, 118087, 354282, 1062869, 3188632, 9565923, 28697798, 86093425, 258280308, 774840959, 2324522914, 6973568781, 20920706384, 62762119195, 188286357630, 564859072937, 1694577218860 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Row sums of triangle A132307.

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (5,-7,3).

FORMULA

Binomial transform of A077552.

a(n) = 2*3^n-n-1. - Rolf Pleisch, Sep 26 2010

G.f.: (1-x+2*x^2)/((1-3*x)*(1-x)^2). - Bruno Berselli, Mar 31 2011

EXAMPLE

a(2) = 15 = sum of row 2 terms of triangle A132307: (7 + 7 + 1).

a(2) = 15 = (1, 2, 1) dot (1, 3, 8) = (1 + 6 + 8); where A077552 = (1, 3, 8, 16, 32, 64,...).

MAPLE

A132308:=n->2*3^n-n-1; seq(A132308(n), n=0..30); # Wesley Ivan Hurt, Mar 26 2014

MATHEMATICA

s=1; lst={s}; Do[s+=(n+=s++)+n; AppendTo[lst, s], {n, 0, 5!, 1}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 15 2008 *)

Table[2*3^n-n-1, {n, 0, 30}] (* or *) LinearRecurrence[{5, -7, 3}, {1, 4, 15}, 30] (* Harvey P. Dale, Aug 06 2013 *)

CoefficientList[Series[(1 - x + 2 x^2)/((1 - 3 x) (1 - x)^2), {x, 0, 50}], x] (* Vincenzo Librandi, Mar 27 2014 *)

CROSSREFS

Cf. A132307, A132309, A077552.

Sequence in context: A053406 A225265 A143215 * A026110 A056327 A026328

Adjacent sequences:  A132305 A132306 A132307 * A132309 A132310 A132311

KEYWORD

nonn

AUTHOR

Gary W. Adamson, Aug 18 2007

EXTENSIONS

More terms from Vladimir Joseph Stephan Orlovsky, Nov 15 2008

Wrong formula 2*n^3-n-1 removed by Rolf Pleisch, Oct 19 2010

Simpler definition from Wesley Ivan Hurt, Mar 26 2014

STATUS

approved

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Last modified December 9 23:16 EST 2016. Contains 278993 sequences.