A123208 Start with 1, then alternately add 2 or double.

1, 3, 6, 8, 16, 18, 36, 38, 76, 78, 156, 158, 316, 318, 636, 638, 1276, 1278, 2556, 2558, 5116, 5118, 10236, 10238, 20476, 20478, 40956, 40958, 81916, 81918, 163836, 163838, 327676, 327678, 655356, 655358, 1310716, 1310718, 2621436, 2621438, 5242876, 5242878

Offset: 0

Author

Philippe Deléham, Oct 04 2006

Keywords

• easy
• nonn

Examples

			1, 1+2=3, 3*2=6, 6+2=8, 8*2=16, ...
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,3,0,-2).

Crossrefs

Cf. A048487, A051633.

Programs

Magma

m:=50; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((1+3*x+3*x^2-x^3)/((1-x^2)*(1-2*x^2)))); // Vincenzo Librandi, Jun 25 2013

Maple

a:=proc(n) if n mod 2 = 0 then 5*2^(n/2)-4 else 5*2^((n-1)/2)-2 fi end: seq(a(n),n=0..45); # Emeric Deutsch, Oct 10 2006

Mathematica

nxt[{a_,b_}]:={b+2,2(b+2)}; Rest[Flatten[NestList[nxt,{1,1},20]]] (* or *) LinearRecurrence[{0,3,0,-2},{1,3,6,8},40] (* Harvey P. Dale, Oct 10 2012 *)
CoefficientList[Series[(1 + 3 x + 3 x^2 - x^3) / ((1 - x) (1 + x) (1 - 2 x^2)), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 25 2013 *)

Formula

a(2n) = 5*2^n - 4; a(2n+1) = 5*2^n - 2 (n >= 0). - Emeric Deutsch, Oct 10 2006

From Colin Barker, Sep 10 2012: (Start)

a(n) = 3*a(n-2) - 2*a(n-4).

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

a(2n) = A048487(n); a(2n+1) = A051633(n). - Philippe Deléham, Apr 15 2013

E.g.f.: 5*cosh(sqrt(2)*x) - 4*cosh(x) + 5*sinh(sqrt(2)*x)/sqrt(2) - 2*sinh(x). - Stefano Spezia, Oct 03 2023

Extensions

More terms from Emeric Deutsch, Oct 10 2006