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

1,2

Comments

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

Links

Table of n, a(n) for n=1..31.

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

Example

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).

Prog

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

Crossrefs

Essentially a duplicate of A051633.

Cf. A133805.

Cf. A083329, A053209.

Sequence in context: A000235 A006478 A104187 * A051633 A172265 A258272

Adjacent sequences: A131048 A131049 A131050 * A131052 A131053 A131054

Keyword

nonn,easy

Author

Gary W. Adamson, Sep 23 2007

Extensions

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

Status

approved