OFFSET
1,4
COMMENTS
See A187180 for details.
LINKS
Ray Chandler, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 0, 1, -1).
FORMULA
After the initial block of three 1's, the sequence is quasi-periodic with period 9, increasing by 3 after each block.
From Colin Barker, Nov 05 2015: (Start)
a(n) = a(n-1) + a(n-9) - a(n-10) for n>12.
G.f.: x*(x^11-x^10-x^8+x^7+x^6+x^3+1) / ((x-1)^2*(x^2+x+1)*(x^6+x^3+1)).
(End)
EXAMPLE
The sequence begins
1 1 1
2 2 2 3 4 3 4 3 4
5 5 5 6 7 6 7 6 7
8 8 8 9 10 9 10 9 10
11 11 11 12 13 12 13 12 13
14 14 14 15 16 15 16 15 16 ...
MATHEMATICA
Join[{1, 1}, LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, 1, -1}, {1, 2, 2, 2, 3, 4, 3, 4, 3, 4}, 98]] (* Ray Chandler, Aug 26 2015 *)
PROG
(PARI) Vec(x*(x^11-x^10-x^8+x^7+x^6+x^3+1)/((x-1)^2*(x^2+x+1)*(x^6+x^3+1)) + O(x^100)) \\ Colin Barker, Nov 05 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Mar 06 2011
STATUS
approved