%I #41 Mar 23 2023 06:49:20

%S 1,3,8,18,38,78,158,318,638,1278,2558,5118,10238,20478,40958,81918,

%T 163838,327678,655358,1310718,2621438,5242878,10485758,20971518,

%U 41943038,83886078,167772158,335544318,671088638,1342177278,2684354558

%N Row sums of triangle A133805.

%C Last digit of a(n) is 8 for n > 2. - _Jon Perry_, Nov 19 2012

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

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

%F a(n) = 5*2^(n-2)-2, n>1. - _Gary Detlefs_, Jun 22 2010

%F a(n) = 2(n-1) + Sum_{i=1..n-1} a(i). - _Jon Perry_, Nov 19 2012

%e a(4) = 18 = sum of row 4 terms of triangle A133805: (7 + 6 + 4 + 1).

%e a(4) = 18 = (1, 3, 3, 1), dot (1, 2, 3, 2) = (1 + 6 + 9 + 2).

%o (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

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 31); Coefficients(R!( (1+x^2)/((1-x)*(1-2*x)))); // _Marius A. Burtea_, Oct 15 2019

%Y Essentially a duplicate of A051633.

%Y Cf. A133805.

%Y Cf. A083329, A053209.

%K nonn,easy

%O 1,2

%A _Gary W. Adamson_, Sep 23 2007

%E More terms from _R. J. Mathar_, Jun 13 2008