OFFSET
1,2
LINKS
Guenther Schrack, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).
FORMULA
a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.
a(n) = floor((5*n-2)/3). - Gary Detlefs, May 14 2011
G.f.: x*(1+x+2*x^2+x^3)/((1+x+x^2)*(1-x)^2). - R. J. Mathar, Oct 08 2011
From Wesley Ivan Hurt, Jun 14 2016: (Start)
a(n) = (15*n - 9 + 2*sqrt(3)*sin(2*n*Pi/3))/9.
a(3k) = 5k - 1, a(3k-1) = 5k - 3, a(3k-2) = 5k - 4. (End)
E.g.f.: (9 + 3*(5*x - 3)*exp(x) + 2*sqrt(3)*sin(sqrt(3)*x/2)*(cosh(x/2) - sinh(x/2)))/9. - Ilya Gutkovskiy, Jun 14 2016
From Guenther Schrack, Oct 31 2019: (Start)
a(n) = a(n-3) + 5 with a(1) = 1, a(2) = 2, a(3) = 4 for n > 3.
a(n) = (15*n - 9 + (w^(2*n) - w^n)*(1 + 2*w))/9 where w = (-1 + sqrt(-3))/2. (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(10-2*sqrt(5))*Pi/10 - log(phi)/sqrt(5) + log(2)/5, where phi is the golden ratio (A001622). - Amiram Eldar, Apr 16 2023
MAPLE
A032793:=n->(15*n-9+2*sqrt(3)*sin(2*n*Pi/3))/9: seq(A032793(n), n=1..100); # Wesley Ivan Hurt, Jun 14 2016
MATHEMATICA
Select[Range[0, 200], MemberQ[{1, 2, 4}, Mod[#, 5]] &] (* Vladimir Joseph Stephan Orlovsky, Feb 11 2012 *)
LinearRecurrence[{1, 0, 1, -1}, {1, 2, 4, 6}, 90] (* Harvey P. Dale, May 20 2019 *)
PROG
(Magma)[ n: n in [0..120] | n mod 5 in {1, 2, 4} ]; // Vincenzo Librandi, Dec 29 2010
(PARI) a(n)=n\3*5+[-1, 1, 2][n%3+1] \\ Charles R Greathouse IV, Jan 18 2012
(Sage) [(15*n - 9 + 2*sqrt(3)*sin(2*n*pi/3))/9 for n in (1..100)] # G. C. Greubel, Nov 06 2019
(GAP) a:=[1, 2, 4, 6];; for n in [5..100] do a[n]:=a[n-1]+a[n-3]-a[n-4]; od; a; # G. C. Greubel, Nov 06 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Patrick De Geest, May 15 1998
EXTENSIONS
Better description from Michael Somos, Jun 08 2000
STATUS
approved