A136488 a(n) = 2^n - A005418(n).
1, 2, 5, 10, 22, 44, 92, 184, 376, 752, 1520, 3040, 6112, 12224, 24512, 49024, 98176, 196352, 392960, 785920, 1572352, 3144704, 6290432, 12580864, 25163776, 50327552, 100659200, 201318400, 402644992, 805289984, 1610596352, 3221192704, 6442418176, 12884836352
Offset: 1
Examples
a(5) = 22 = 2^5 - A005418(5) = 32 - 10. a(5) = 22 = sum of row 5 terms of triangle A136482 = (1 + 6 + 8 + 6 + 1).
Links
- Colin Barker, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (2,2,-4).
Programs
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Magma
[2^n - (2^(n - 2) + 2^(Floor(n/2) - 1)): n in [1..40]]; // G. C. Greubel, Nov 02 2018
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Mathematica
Table[2^n - (2^(n - 2) + 2^(Floor[n/2] - 1)), {n, 40}] (* after Harvey P. Dale at A005418, or *) CoefficientList[Series[(1 - x^2)/(1 - 2 x - 2 x^2 + 4 x^3), {x, 0, 40}], x] (* Michael De Vlieger, Sep 23 2016 *) -
PARI
Vec(x*(1-x)*(1+x)/((1-2*x)*(1-2*x^2)) + O(x^40)) \\ Colin Barker, Sep 23 2016
Formula
G.f.: x*(1 - x^2)/(1 - 2*x - 2*x^2 + 4*x^3). - Michael De Vlieger, Sep 23 2016
From Colin Barker, Sep 23 2016: (Start)
a(n) = 3*2^(n-2)-2^(n/2-1) for n even.
a(n) = 3*2^(n-2)-2^((n-3)/2) for n odd.
(End)
a(n) = A135098(n-1) for n >= 1. - Georg Fischer, Nov 02 2018
Extensions
More terms from Colin Barker, Mar 19 2013
Missing a(4) added by Michael De Vlieger, Sep 23 2016