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A134062 Row sums of triangle A134061.

%I A134062 #26 Dec 17 2024 18:44:21
%S A134062 1,8,18,38,78,158,318,638,1278,2558,5118,10238,20478,40958,81918,
%T A134062 163838,327678,655358,1310718,2621438,5242878,10485758,20971518,
%U A134062 41943038,83886078,167772158,335544318,671088638,1342177278,2684354558,5368709118,10737418238
%N A134062 Row sums of triangle A134061.
%C A134062 a(n) = bottom term of the matrix-vector product M^n*V, where M = the 3 X 3 matrix [1,0,0; 0,1,0; 1,1,2] and V = [1,1,3].
%C A134062 Binomial transform of (1,7,3,7,3,7,3,...).
%C A134062 Essentially the same as A131051 and A051633. - _R. J. Mathar_, Mar 28 2012
%H A134062 Colin Barker, <a href="/A134062/b134062.txt">Table of n, a(n) for n = 0..1000</a>
%H A134062 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F A134062 For n > 0, a(n) = 5*2^n - 2. - _Vaclav Kotesovec_, Jan 26 2015
%F A134062 From _Colin Barker_, Nov 17 2015: (Start)
%F A134062 a(n) = 3*a(n-1) - 2*a(n-2) for n>2.
%F A134062 G.f.: -(4*x^2-5*x-1) / ((x-1)*(2*x-1)). (End)
%e A134062 a(2) = 18 = sum of row 2 terms, triangle A134061: (3 + 10 + 5).
%e A134062 a(3) = 38 = (1, 3, 3, 1) dot (1, 7, 3, 7) = (1 + 21 + 9 + 7).
%t A134062 a=8; lst={1, a}; k=10; Do[a+=k; AppendTo[lst, a]; k+=k, {n, 0, 5!}]; lst (* _Vladimir Joseph Stephan Orlovsky_, Dec 17 2008 *)
%t A134062 Flatten[{1, Table[5*2^n-2, {n, 1, 40}]}] (* _Vaclav Kotesovec_, Jan 26 2015 *)
%t A134062 LinearRecurrence[{3,-2},{1,8,18},40] (* _Harvey P. Dale_, Dec 17 2024 *)
%o A134062 (PARI) Vec(-(4*x^2-5*x-1)/((x-1)*(2*x-1)) + O(x^100)) \\ _Colin Barker_, Nov 17 2015
%Y A134062 Cf. A134061.
%K A134062 nonn,easy
%O A134062 0,2
%A A134062 _Gary W. Adamson_, Oct 05 2007
%E A134062 More terms from _Jon E. Schoenfield_, Jan 25 2015