A166523 a(n) = 8*n - a(n-1), with n>1, a(1)=1.
1, 15, 9, 23, 17, 31, 25, 39, 33, 47, 41, 55, 49, 63, 57, 71, 65, 79, 73, 87, 81, 95, 89, 103, 97, 111, 105, 119, 113, 127, 121, 135, 129, 143, 137, 151, 145, 159, 153, 167, 161, 175, 169, 183, 177, 191, 185, 199, 193, 207, 201, 215, 209, 223, 217, 231, 225, 239, 233
Offset: 1
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
Programs
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Magma
[n eq 1 select 1 else 8*n-Self(n-1): n in [1..70]]; // Vincenzo Librandi, Sep 13 2013
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Mathematica
CoefficientList[Series[(1 +14 x -7 x^2)/((1+x) (1-x)^2), {x,0,60}], x] (* Vincenzo Librandi, Sep 13 2013 *) -
SageMath
def A166523(n): return 4*n - 3 + 10*((n+1)%2) [A166523(n) for n in range(1,101)] # G. C. Greubel, Aug 03 2024
Formula
G.f.: x*(1+14*x-7*x^2) / ( (1+x)*(1-x)^2 ). - R. J. Mathar, Mar 08 2011
From G. C. Greubel, May 16 2016: (Start)
E.g.f.: 5*exp(-x) + 2*(1 + 2*x)*exp(x) - 7.
a(n) = a(n-1) + a(n-2) - a(n-3). (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = 1/7 + (1/8 + 1/(4*sqrt(2)))*Pi. - Amiram Eldar, Feb 24 2023
a(n) = 4*n + 2 + 5*(-1)^n. - G. C. Greubel, Aug 03 2024