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a(n) = Sum_{k=0..n} A026615(n, k).
18

%I #39 Jun 24 2024 04:11:45

%S 1,2,5,12,26,54,110,222,446,894,1790,3582,7166,14334,28670,57342,

%T 114686,229374,458750,917502,1835006,3670014,7340030,14680062,

%U 29360126,58720254,117440510,234881022,469762046,939524094,1879048190,3758096382,7516192766

%N a(n) = Sum_{k=0..n} A026615(n, k).

%C In general, a first order inhomogeneous recurrence of the form s(0) = a, s(n) = m*s(n-1) + k, n>0, will have a closed form of a*m^n +((m^n-1)/(m-1))*k. - _Gary Detlefs_, Jun 07 2024

%H Colin Barker, <a href="/A026622/b026622.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).

%F a(n) = 7 * 2^(n-2) - 2, a(0) = 1, a(1) = 2 (Cf. A026624). - _Ralf Stephan_, Feb 05 2004

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

%F From _Colin Barker_, Feb 17 2016: (Start)

%F a(n) = 3*a(n-1) - 2*a(n-2) for n>3.

%F G.f.: (1 - x + x^2 + x^3)/((1 - x)*(1 - 2*x)). (End)

%F E.g.f.: (1/4)*( 5 + 2*x - 8*exp(x) + 7*exp(2*x) ). - _G. C. Greubel_, Jun 24 2024

%t Table[7*2^(n-2) -2 +Boole[n==1]/2 +(5/4)*Boole[n==0], {n,0,40}] (* _G. C. Greubel_, Jun 24 2024 *)

%o (PARI) Vec((1-x+x^2+x^3)/((1-x)*(1-2*x)) + O(x^40)) \\ _Colin Barker_, Feb 17 2016

%o (Magma) [n le 1 select n+1 else 7*2^(n-2) -2: n in [0..40]]; // _G. C. Greubel_, Jun 24 2024

%o (SageMath) [(7*2^n -8 +2*int(n==1) +5*int(n==0))/4 for n in range(41)] # _G. C. Greubel_, Jun 24 2024

%Y Cf. A026615, A026616, A026617, A026618, A026619, A026620, A026621.

%Y Cf. A026623, A026624, A026625, A026956, A026957, A026958, A026959.

%Y Cf. A026960.

%K nonn,easy

%O 0,2

%A _Clark Kimberling_