OFFSET
1,2
COMMENTS
LINKS
Guenther Schrack, Table of n, a(n) for n = 1..10010
Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).
FORMULA
G.f.: x^2*(3+x+x^2+x^3)/((1+x)*(1+x^2)*(1-x)^2). - R. J. Mathar, Oct 08 2011
From Wesley Ivan Hurt, Jun 02 2016: (Start)
a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
a(n) = (6*n - 3 + i^(2*n) - (1+i)*i^(-n) - (1-i)*i^n)/4 where i=sqrt(-1).
E.g.f.: (2 - sin(x) - cos(x) + (3*x - 2)*sinh(x) + (3*x - 1)*cosh(x))/2. - Ilya Gutkovskiy, Jun 02 2016
From Guenther Schrack, Feb 15 2019: (Start)
a(n) = (6*n - 3 + (-1)^n - 2*(-1)^(n*(n-1)/2))/4.
a(n) = a(n-4) + 6, a(1)=0, a(2)=3, a(3)=4, a(4)=5, for n > 4.
a(-n) = -A047246(n+2). (End)
Sum_{n>=2} (-1)^n/a(n) = 2*log(2)/3 - Pi/(6*sqrt(3)). - Amiram Eldar, Dec 17 2021
MAPLE
A047250:=n->(6*n-3+I^(2*n)-(1+I)*I^(-n)-(1-I)*I^n)/4: seq(A047250(n), n=1..100); # Wesley Ivan Hurt, Jun 02 2016
MATHEMATICA
Select[Range[0, 100], MemberQ[{0, 3, 4, 5}, Mod[#, 6]]&] (* or *) LinearRecurrence[{1, 0, 0, 1, -1}, {0, 3, 4, 5, 6}, 60] (* Harvey P. Dale, Apr 01 2013 *)
PROG
(Magma) [n : n in [0..150] | n mod 6 in [0, 3, 4, 5]]; // Wesley Ivan Hurt, Jun 02 2016
(PARI) my(x='x+O('x^70)); concat([0], Vec(x^2*(3+x+x^2+x^3)/((1+x)*(1+x^2)*(1-x)^2))) \\ G. C. Greubel, Feb 16 2019
(Sage) a=(x^2*(3+x+x^2+x^3)/((1+x)*(1+x^2)*(1-x)^2)).series(x, 72).coefficients(x, sparse=False); a[1:] # G. C. Greubel, Feb 16 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved