A144414 a(n) = 2*(4^n - 1)/3 - n.

1, 8, 39, 166, 677, 2724, 10915, 43682, 174753, 699040, 2796191, 11184798, 44739229, 178956956, 715827867, 2863311514, 11453246105, 45812984472, 183251937943, 733007751830, 2932031007381, 11728124029588, 46912496118419

Offset: 1

Author

Roger L. Bagula and Gary W. Adamson, Oct 01 2008

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-9,4).

Crossrefs

Cf. A142458, A142976, A144380.

Programs

Magma

[(2^(2*n+1) -3*n -2)/3: n in [1..50]]; // G. C. Greubel, Mar 28 2021

Mathematica

Table[2(4^n-1)/3 -n,{n,30}] (* or *) LinearRecurrence[{6,-9,4},{1,8,39},30] (* Harvey P. Dale, Mar 17 2015 *)

Sage

[(2^(2*n+1) -3*n -2)/3 for n in (1..50)] # G. C. Greubel, Mar 28 2021

Formula

a(n) = A142458(n+1,n).

a(n) = A020988(n) - n. - R. J. Mathar, Nov 21 2008

G.f.: x*(1+2*x)/((1-x)^2*(1-4*x)). - Colin Barker, Jan 11 2012

a(1)=1, a(2)=8, a(3)=39, a(n) = 6*a(n-1) - 9*a(n-2) + 4*a(n-3). - Harvey P. Dale, Mar 17 2015

E.g.f.: (1/3)*(-2 - 3*x + 2*exp(x))*exp(x). - G. C. Greubel, Mar 28 2021