A168409 a(n) = 8 + 9*floor((n-1)/2).

8, 8, 17, 17, 26, 26, 35, 35, 44, 44, 53, 53, 62, 62, 71, 71, 80, 80, 89, 89, 98, 98, 107, 107, 116, 116, 125, 125, 134, 134, 143, 143, 152, 152, 161, 161, 170, 170, 179, 179, 188, 188, 197, 197, 206, 206, 215, 215, 224, 224, 233, 233, 242, 242, 251, 251, 260

Offset: 1

Author

Vincenzo Librandi, Nov 25 2009

Keywords

• nonn
• easy
• less

Comments

Old definition: "a(n)=9*n-a(n-1)-2 (with a(1)=8)".

The sequences generated by the recursive relation b(n) = h*n-b(n-1)+k, with b(1)=c and h, k, c prefixed integers, satisfy the formula b(n) = c + h*floor((n-1)/2) when 2*h+k = 2*c. - Bruno Berselli, Sep 18 2013

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. A017257.

Programs

Magma

[8+9*Floor((n-1)/2): n in [1..70]]; // Vincenzo Librandi, Sep 18 2013

Mathematica

RecurrenceTable[{a[1]==8,a[n]==9n-a[n-1]-2},a,{n,60}] (* or *) LinearRecurrence[{1,1,-1},{8,8,17},80] (* or *) With[{c = LinearRecurrence[{2,-1},{8,17},30]},Riffle[c,c]] (* Harvey P. Dale, Aug 18 2013 *)
CoefficientList[Series[(8 + x^2)/((1 + x) (x - 1)^2), {x, 0, 70}], x] (* Vincenzo Librandi, Sep 18 2013 *)

PARI

a(n)=(n-1)\2*9 + 8 \\ Charles R Greathouse IV, Jul 21 2016

Formula

a(n) = 9*n - a(n-1) - 2, with n>1, a(1)=8.

a(1)=8, a(2)=8, a(3)=17; for n>1, a(n) = a(n-1) +a(n-2) -a(n-3). - Harvey P. Dale, Aug 18 2013

G.f.: x*(8 + x^2)/((1+x)*(x-1)^2). - Vincenzo Librandi, Sep 18 2013

E.g.f.: (1/4)*(-9 + 4*exp(x) + (5 + 18*x)*exp(2*x))*exp(-x). - G. C. Greubel, Jul 21 2016

Extensions

New definition by Vincenzo Librandi, Sep 18 2013