A132308 a(n) = 2*3^n - n - 1.

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

Offset: 0

Author

Gary W. Adamson, Aug 18 2007

Keywords

• nonn

Comments

Row sums of triangle A132307.

Examples

			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, ...).
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-7,3).

Crossrefs

Cf. A132307, A132309, A077552.

Programs

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 *)

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

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