OFFSET
0,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).
FORMULA
G.f.: (1 + x + x^3)/((1 - x)*(1 - x^4)).
a(n) = floor((3*n + 5)/4).
a(n) = a(n-1) + a(n-4) - a(n-5) for n>4, with a(0)=1, a(1)=2, a(2)=2, a(3)=3, a(4)=4. - Harvey P. Dale, Apr 01 2013
a(n) = (6*n+7+2*cos(n*Pi/2)+cos((n+1)*Pi)+2*sin(n*Pi/2))/8. - Wesley Ivan Hurt, Oct 01 2017
Sum_{n>=0} (-1)^n/a(n) = log(3)/2 + Pi/(6*sqrt(3)). - Amiram Eldar, Jan 31 2023
MAPLE
MATHEMATICA
CoefficientList[ Series[ (1 + x + x^3)/((1 - x)*(1 - x^4)), {x, 0, 75} ], x] (* or *) Table[Floor[(3 n + 5)/4], {n, 0, 75}]
LinearRecurrence[{1, 0, 0, 1, -1}, {1, 2, 2, 3, 4}, 80] (* Harvey P. Dale, Apr 01 2013 *)
PROG
(Magma) [Floor((3*n + 5)/4): n in [0..100]]; // Wesley Ivan Hurt, Jan 02 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Robert G. Wilson v, Jan 06 2002
STATUS
approved