OFFSET
0,3
COMMENTS
List of quadruples [5*k, 5*k, 5*k+2, 5*k+3]. - Luce ETIENNE, Aug 14 2017
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).
FORMULA
a(n) = (10*n-5+3*cos(n*Pi)+2*(cos(n*Pi/2)-sin(n*Pi/2)))/8. - Luce ETIENNE, Aug 14 2017
From Colin Barker, Aug 14 2017: (Start)
G.f.: x^2*(2 + x + 2*x^2) / ((1 - x)^2*(1 + x)*(1 + x^2)).
a(n) = a(n-1) + a(n-4) - a(n-5) for n>4.
(End)
MATHEMATICA
Table[Floor[n/2]+Floor[3n/4], {n, 0, 120}]
LinearRecurrence[{1, 0, 0, 1, -1}, {0, 0, 2, 3, 5}, 80] (* Harvey P. Dale, Dec 05 2018 *)
PROG
(PARI) a(n) = n\2 + 3*n\4; \\ Altug Alkan, Aug 14 2017
(PARI) concat(vector(2), Vec(x^2*(2 + x + 2*x^2) / ((1 - x)^2*(1 + x)*(1 + x^2)) + O(x^100))) \\ Colin Barker, Aug 14 2017
(Python)
def A187322(n): return (n>>1)+(3*n>>2) # Chai Wah Wu, Jan 31 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Mar 08 2011
STATUS
approved