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

1,2

Links

David Lovler, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

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

Mathematica

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

Prog

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

Crossrefs

Union of A017077 and A017089.

Cf. A047467.

Sequence in context: A058890 A369205 A306998 * A032929 A226832 A320919

Adjacent sequences: A047465 A047466 A047467 * A047469 A047470 A047471

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, Aug 06 2010

Status

approved