A101351 a(n) = 2^n-1 + Fibonacci(n).
2, 4, 9, 18, 36, 71, 140, 276, 545, 1078, 2136, 4239, 8424, 16760, 33377, 66522, 132668, 264727, 528468, 1055340, 2108097, 4212014, 8417264, 16823583, 33629456, 67230256, 134414145, 268753266, 537385140, 1074573863, 2148829916, 4297145604, 8593459169
Offset: 1
Links
- Colin Barker, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (4,-4,-1,2).
Programs
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Maple
seq(2^x-1+fibonacci(x),x=1..30);
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Mathematica
Table[2^n-1+Fibonacci[n],{n,30}] (* or *) LinearRecurrence[{4,-4,-1,2},{2,4,9,18},30] (* Harvey P. Dale, Aug 24 2012 *) -
PARI
Vec(x*(2-4*x+x^2)/((1-x)*(1-2*x)*(1-x-x^2)) + O(x^30)) \\ Colin Barker, Nov 02 2016
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Sage
[gaussian_binomial(n,1,2)+fibonacci (n) for n in range(1,31)] # Zerinvary Lajos, May 29 2009
Formula
a(n) = 4*a(n-1) -4*a(n-2) -a(n-3) +2*a(n-4). G.f.: x*(2-4*x+x^2)/((x-1) * (2*x-1) * (1-x-x^2)). - R. J. Mathar, Feb 06 2010
a(n) = ((1+sqrt(5))^n-(1-sqrt(5))^n)/(2^n*sqrt(5)) + 2^n - 1. - Colin Barker, Nov 02 2016
Extensions
Offset changed to 1 by Colin Barker, Nov 02 2016