A047468 Numbers that are congruent to {1, 2} mod 8.

1, 2, 9, 10, 17, 18, 25, 26, 33, 34, 41, 42, 49, 50, 57, 58, 65, 66, 73, 74, 81, 82, 89, 90, 97, 98, 105, 106, 113, 114, 121, 122, 129, 130, 137, 138, 145, 146, 153, 154, 161, 162, 169, 170, 177, 178, 185, 186, 193, 194, 201, 202, 209, 210, 217, 218, 225, 226, 233

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

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

Crossrefs

Union of A017077 and A017089.

Cf. A047467.

Programs

Mathematica

Flatten[#+{1,2}&/@(8Range[0,30])] (* or *) LinearRecurrence[{1,1,-1},{1,2,9},60] (* Harvey P. Dale, Mar 26 2013 *)

PARI

a(n)=(n-1)\2*8+2-n%2 \\ Charles R Greathouse IV, May 14 2012

Formula

a(n) = 8*n - a(n-1) - 13 (with a(1)=1). - Vincenzo Librandi, Aug 06 2010

G.f.: x*(1+x+6*x^2)/((1-x)^2*(1+x)). - Colin Barker, May 13 2012

a(n) = 1 + 8*floor((n-1)/2) + ((n-1) mod 2). - Alois P. Heinz, May 13 2012

a(n) = (-3*(3 + (-1)^n) + 8*n)/2. - Colin Barker, May 14 2012

a(1)=1, a(2)=2, a(3)=9, a(n) = a(n-1) + a(n-2) - a(n-3). - Harvey P. Dale, Mar 26 2013

Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(2)*Pi/16 + log(2)/8 + sqrt(2)*log(sqrt(2)+1)/8. - Amiram Eldar, Dec 18 2021

E.g.f.: 6 + ((8*x - 9)*exp(x) - 3*exp(-x))/2. - David Lovler, Sep 02 2022

Extensions

More terms from Vincenzo Librandi, Aug 06 2010