%I #54 Sep 06 2016 10:49:11
%S 2,6,13,26,51,100,197,390,775,1544,3081,6154,12299,24588,49165,98318,
%T 196623,393232,786449,1572882,3145747,6291476,12582933,25165846,
%U 50331671,100663320,201326617,402653210,805306395,1610612764,3221225501,6442450974,12884901919,25769803808,51539607585,103079215138,206158430243,412316860452,824633720869
%N a(n) = 3*2^n + n - 1.
%H Carauleanu Marc, <a href="/A275970/b275970.txt">Table of n, a(n) for n = 0..400</a>
%H S. W. Golomb, <a href="http://www.jstor.org/stable/2005337">Properties of the sequence 3.2^n+1</a>, Math. Comp., 30 (1976), 657-663.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,-5,2).
%F a(n) = 2*a(n-1) - n + 2.
%F a(n+1) - a(n) = A181565(n)
%F a(n) = A007283(n) + n - 1
%F a(n) = A083706(n) + A000079(n)
%F a(n) = A145071(n+1) - A000079(n)
%F a(n) = A079583(n) + A005408(n)
%F a(n) = A068156(n+1) - A079583(n)
%F a(n) = (A068156(n+1) + A005408(n)) / 2
%F a(n) = A000225(n) + A000325(n+1) + A005408(n)
%F a(n) = A068156(n+1) - A000225(n) - A000325(n+1)
%F a(n) = A068156(n+1) - A007283(n) + n + 2.
%F a(n) = A000079(n) + A000225(n) + A000295(n) + A005408(n)
%F From _G. C. Greubel_, Aug 18 2016: (Start)
%F O.g.f.: (2 - 2*x - x^2)/( (1-2*x)*(1-x)^2 ).
%F E.g.f.: 3*exp(2*x) + (x-1)*exp(x).
%F a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-2). (End)
%t LinearRecurrence[{4,-5,2},{2,6,13}, 25] (* or *) Table[3*2^n + n - 1, {n,0,25}] (* _G. C. Greubel_, Aug 18 2016 *)
%o (PARI) a(n)=3*2^n+n-1 \\ _Charles R Greathouse IV_, Aug 27 2016
%K nonn,easy
%O 0,1
%A _Miquel Cerda_, Aug 15 2016