A131051 Row sums of triangle A133805.

1, 3, 8, 18, 38, 78, 158, 318, 638, 1278, 2558, 5118, 10238, 20478, 40958, 81918, 163838, 327678, 655358, 1310718, 2621438, 5242878, 10485758, 20971518, 41943038, 83886078, 167772158, 335544318, 671088638, 1342177278, 2684354558

Offset: 1

Author

Gary W. Adamson, Sep 23 2007

Keywords

• nonn
• easy

Comments

Last digit of a(n) is 8 for n > 2. - Jon Perry, Nov 19 2012

Examples

			a(4) = 18 = sum of row 4 terms of triangle A133805: (7 + 6 + 4 + 1).
a(4) = 18 = (1, 3, 3, 1), dot (1, 2, 3, 2) = (1 + 6 + 9 + 2).
		

Crossrefs

Essentially a duplicate of A051633.

Cf. A133805.

Cf. A083329, A053209.

Programs

Magma

a:=[1]; for n in [2..31] do Append(~a,2*n-2+&+[a[i]:i in [1..n-1]]); end for; a; // Marius A. Burtea, Oct 15 2019

Magma

R:=PowerSeriesRing(Integers(), 31); Coefficients(R!( (1+x^2)/((1-x)*(1-2*x)))); // Marius A. Burtea, Oct 15 2019

Formula

Binomial transform of [1, 2, 3, 2, 3, 2, 3, ...].

O.g.f.: (1+x^2)/((1-x)(1-2*x)). a(n)=A051633(n-2). - R. J. Mathar, Jun 13 2008

a(n) = 5*2^(n-2)-2, n>1. - Gary Detlefs, Jun 22 2010

a(n) = 2(n-1) + Sum_{i=1..n-1} a(i). - Jon Perry, Nov 19 2012

Extensions

More terms from R. J. Mathar, Jun 13 2008