A166539 a(n) = (10*n + 7*(-1)^n + 5)/4.

2, 8, 7, 13, 12, 18, 17, 23, 22, 28, 27, 33, 32, 38, 37, 43, 42, 48, 47, 53, 52, 58, 57, 63, 62, 68, 67, 73, 72, 78, 77, 83, 82, 88, 87, 93, 92, 98, 97, 103, 102, 108, 107, 113, 112, 118, 117, 123, 122, 128, 127, 133, 132, 138, 137, 143, 142, 148, 147, 153, 152, 158

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, A166526.

Programs

Magma

[5*n/2 + (5+7*(-1)^n)/4: n in [1..70]]; // Vincenzo Librandi, May 15 2013

Mathematica

RecurrenceTable[{a[1]==2,a[n]==5n-a[n-1]},a[n],{n,70}] (* or *) LinearRecurrence[{1,1,-1},{2,8,7},70] (* Harvey P. Dale, Jun 29 2011 *)

SageMath

def A166539(n): return (5*n - 1 + 7*((n+1)%2))//2
[A166539(n) for n in range(1, 101)] # G. C. Greubel, Aug 04 2024

Formula

a(n) = 5*n - a(n-1), n>=2.

From Harvey P. Dale, Jun 29 2011: (Start)

a(n) = a(n-1) + a(n-2) - a(n-3), n>=4.

G.f.: x*(2+3*x*(2-x))/((1-x)^2*(1+x)). (End)

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

E.g.f.: (1/4)*(5*(1 + 2*x)*exp(x) + 7*exp(-x) - 12).

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

Sum_{n>=1} (-1)^(n+1)/a(n) = 1/3 + sqrt((5-2*sqrt(5))/5)*Pi/5. - Amiram Eldar, Feb 24 2023

a(n) = A166520(n) - (-1)^n. - G. C. Greubel, Aug 04 2024