A166524 a(n) = 9*n - a(n-1), with n>1, a(1)=1.

1, 17, 10, 26, 19, 35, 28, 44, 37, 53, 46, 62, 55, 71, 64, 80, 73, 89, 82, 98, 91, 107, 100, 116, 109, 125, 118, 134, 127, 143, 136, 152, 145, 161, 154, 170, 163, 179, 172, 188, 181, 197, 190, 206, 199, 215, 208, 224, 217, 233, 226, 242, 235, 251, 244, 260, 253

Offset: 1

Author

Vincenzo Librandi, Oct 16 2009

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Crossrefs

Cf. A166519, A166520, A166521, A166522, A166523, A166525, A166526.

Programs

Magma

[n eq 1 select 1 else 9*n-Self(n-1): n in [1..80]]; // Vincenzo Librandi, Sep 13 2013

Mathematica

CoefficientList[Series[(1 +16 x -8 x^2)/((1+x) (1-x)^2), {x,0,80}], x] (* Vincenzo Librandi, Sep 13 2013 *)
LinearRecurrence[{1,1,-1},{1,17,10},60] (* Harvey P. Dale, Dec 24 2014 *)

SageMath

def A166524(n): return (9*n - 7 + 23*((n+1)%2))//2
[A166524(n) for n in range(1, 101)] # G. C. Greubel, Aug 04 2024

Formula

G.f.: x*(1+16*x-8*x^2) / ( (1+x)*(1-x)^2 ). - R. J. Mathar, Mar 08 2011

From G. C. Greubel, May 16 2016: (Start)

E.g.f.: (1/4)*(23*exp(-x) + 9*(1 + 2*x)*exp(x) - 32).

a(n) = a(n-1) + a(n-2) - a(n-3). (End)

Sum_{n>=1} (-1)^(n+1)/a(n) = 1/8 + cot(Pi/9)*Pi/9. - Amiram Eldar, Feb 24 2023

a(n) = (1/4)*(18*n + 9 + 23*(-1)^n). - G. C. Greubel, Aug 04 2024