A166526 a(n) = 12*n - a(n-1), with n>1, a(1)=1.

1, 23, 13, 35, 25, 47, 37, 59, 49, 71, 61, 83, 73, 95, 85, 107, 97, 119, 109, 131, 121, 143, 133, 155, 145, 167, 157, 179, 169, 191, 181, 203, 193, 215, 205, 227, 217, 239, 229, 251, 241, 263, 253, 275, 265, 287, 277, 299, 289, 311, 301, 323, 313, 335, 325, 347

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, A166524, A166525.

Programs

Magma

[n eq 1 select 1 else 12*n-Self(n-1): n in [1..80]]; // Vincenzo Librandi, Sep 13 2013

Mathematica

RecurrenceTable[{a[1]==1,a[n]==12n-a[n-1]},a[n],{n,60}] (* or *) LinearRecurrence[{1,1,-1},{1,23,13},60] (* Harvey P. Dale, Aug 10 2011 *)
CoefficientList[Series[(1 + 22 x - 11 x^2) / ((x - 1)^2 (1 + x)), {x, 0, 60}], x] (* Vincenzo Librandi, Sep 13 2013 *)

SageMath

def A166526(n): return 6*n - 5 + 16*((n+1)%2)
[A166526(n) for n in range(1, 101)] # G. C. Greubel, Aug 04 2024

Formula

From Harvey P. Dale, Aug 10 2011: (Start)

a(n) = a(n-1) + a(n-2) - a(n-3), a(1)=1, a(2)=23, a(3)=13, for n>3.

G.f.: x*(1+22*x-11*x^2)/((x-1)^2*(1+x)). (End)

E.g.f.: 8*exp(-x) + 3*(1 + 2*x)*exp(x) - 11. - G. C. Greubel, May 16 2016

Sum_{n>=1} (-1)^(n+1)/a(n) = 1/11 + (1/6 + 1/(4*sqrt(3)))*Pi. - Amiram Eldar, Feb 24 2023

a(n) = 6*n + 3 + 8*(-1)^n. - G. C. Greubel, Aug 04 2024