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
Links
- Index entries for linear recurrences with constant coefficients, signature (0,4,0,-5,0,2).
Programs
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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) = 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
Comments