A147678 Double, add 0, double, add 1, double, add 2, double, add 3, etc.

1, 2, 2, 4, 5, 10, 12, 24, 27, 54, 58, 116, 121, 242, 248, 496, 503, 1006, 1014, 2028, 2037, 4074, 4084, 8168, 8179, 16358, 16370, 32740, 32753, 65506, 65520, 131040, 131055, 262110, 262126, 524252, 524269, 1048538, 1048556, 2097112, 2097131

Offset: 1

Author

N. J. A. Sloane, Apr 21 2009

Keywords

• nonn
• easy

Comments

A147675-A147678 are from a quiz that someone asked me to help them with.

Links

• Index entries for linear recurrences with constant coefficients, signature (0,4,0,-5,0,2).

Programs

Mathematica

Transpose[NestList[Flatten[{Rest[#],2First[#]-5#[[3]]+ 4#[[5]]}]&,{1,2,2,4,5,10},40]][[1]] (* Harvey P. Dale, Mar 24 2011 *)
dp[a_,n_]:=Flatten[{{x=a},Table[{2x,x=2x+m},{m,0,n}]}]; A147678=dp[1,20] (* Zak Seidov, Mar 24 2011 *)
LinearRecurrence[{0, 4, 0, -5, 0, 2}, {1, 2, 2, 4, 5, 10}, 20] (* T. D. Noe, Mar 25 2011 *)

Formula

From R. J. Mathar, Apr 22 2009: (Start)

a(n) = 4*a(n-2) - 5*a(n-4) + 2*a(n-6).

G.f.: -x*(2*x+1)*(2*x^4 - 2*x^2 + 1)/((2*x^2-1)*(x-1)^2*(1+x)^2).

a(n)=(1 + (-1)^n)/2 + 2*A016116(n) - A105811(n+3)/4 - 3*(n+1)/4. (End)

a(n) = 2*a(n-1) - (n mod 2)*(a(n-1) - (n-3)/2). - Reinhard Zumkeller, Apr 22 2009

Extensions

More terms from R. J. Mathar, Apr 22 2009