|
%I #37 Sep 03 2022 08:50:21
%S 5,7,13,15,21,23,29,31,37,39,45,47,53,55,61,63,69,71,77,79,85,87,93,
%T 95,101,103,109,111,117,119,125,127,133,135,141,143,149,151,157,159,
%U 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
%N Numbers that are congruent to {5, 7} mod 8.
%H Colin Barker, <a href="/A047550/b047550.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F a(n) = 8*n-a(n-1)-4 (with a(1)=5). - _Vincenzo Librandi_, Aug 06 2010
%F a(n) = 4*n-(-1)^n. - _Rolf Pleisch_, Nov 02 2010
%F 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
%F G.f.: x*(5+2*x+x^2) / ((1-x)^2*(1+x)). - _Colin Barker_, Aug 26 2016
%F Sum_{n>=1} (-1)^(n+1)/a(n) = Pi/8 - sqrt(2)*log(sqrt(2)+1)/4. - _Amiram Eldar_, Dec 19 2021
%F E.g.f.: 1 + 4*x*exp(x) - exp(-x). - _David Lovler_, Sep 02 2022
%p A047550:=n->4*n-(-1)^n; seq(A047550(n), n=1..100); # _Wesley Ivan Hurt_, Mar 31 2014
%t 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 *)
%t Table[4 n - (-1)^n, {n, 100}] (* _Wesley Ivan Hurt_, Mar 31 2014 *)
%o (PARI) Vec(x*(5+2*x+x^2)/((1-x)^2*(1+x)) + O(x^100)) \\ _Colin Barker_, Aug 26 2016
%Y Union of A004770 and A004771.
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_
%E More terms from _Vincenzo Librandi_, Aug 06 2010
|
