A047550 Numbers that are congruent to {5, 7} mod 8.

5, 7, 13, 15, 21, 23, 29, 31, 37, 39, 45, 47, 53, 55, 61, 63, 69, 71, 77, 79, 85, 87, 93, 95, 101, 103, 109, 111, 117, 119, 125, 127, 133, 135, 141, 143, 149, 151, 157, 159, 165, 167, 173, 175, 181, 183, 189, 191, 197, 199, 205, 207, 213, 215, 221, 223, 229, 231, 237, 239, 245, 247, 253, 255, 261

Offset

1,1

Links

Colin Barker, 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)-4 (with a(1)=5). - Vincenzo Librandi, Aug 06 2010

a(n) = 4*n-(-1)^n. - Rolf Pleisch, Nov 02 2010

a(1)=5, a(2)=7, a(3)=13; for n>3, a(n) = a(n-1)+a(n-2)-a(n-3). - Harvey P. Dale, Jun 04 2012

G.f.: x*(5+2*x+x^2) / ((1-x)^2*(1+x)). - Colin Barker, Aug 26 2016

Sum_{n>=1} (-1)^(n+1)/a(n) = Pi/8 - sqrt(2)*log(sqrt(2)+1)/4. - Amiram Eldar, Dec 19 2021

E.g.f.: 1 + 4*x*exp(x) - exp(-x). - David Lovler, Sep 02 2022

Maple

A047550:=n->4*n-(-1)^n; seq(A047550(n), n=1..100); # Wesley Ivan Hurt, Mar 31 2014

Mathematica

With[{r8=8*Range[0, 40]}, Sort[Join[r8+5, r8+7]]] (* or *) LinearRecurrence[ {1, 1, -1}, {5, 7, 13}, 80] (* Harvey P. Dale, Jun 04 2012 *)
Table[4 n - (-1)^n, {n, 100}] (* Wesley Ivan Hurt, Mar 31 2014 *)

Prog

(PARI) Vec(x*(5+2*x+x^2)/((1-x)^2*(1+x)) + O(x^100)) \\ Colin Barker, Aug 26 2016

Crossrefs

Union of A004770 and A004771.

Sequence in context: A055052 A314314 A314315 * A179194 A314316 A314317

Adjacent sequences: A047547 A047548 A047549 * A047551 A047552 A047553

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, Aug 06 2010

Status

approved