OFFSET
1,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,1,-1).
FORMULA
From Chai Wah Wu, May 30 2016: (Start)
G.f.: x^2*(x^6 + x^5 + x^4 + x^3 + x^2 + 2*x + 1)/(x^8 - x^7 - x + 1).
a(n) = a(n-1) + a(n-7) - a(n-8) for n>8. (End)
From Wesley Ivan Hurt, Jul 21 2016: (Start)
a(n) = a(n-7) + 8 for n>7.
a(n) = (56*n - 42 + (n mod 7) + ((n+1) mod 7) + ((n+2) mod 7) + ((n+3) mod 7) - 6*((n+4) mod 7) + ((n+5) mod 7) + ((n+6) mod 7))/49.
a(7*k) = 8*k-1, a(7*k-1) = 8*k-2, a(7*k-2) = 8*k-3, a(7*k-3) = 8*k-4, a(7*k-4) = 8*k-5, a(7*k-5) = 8*k-7, a(7*k-6) = 8*k-8. (End)
MAPLE
A047565:=n->8*floor(n/7)+[0, 1, 3, 4, 5, 6, 7][(n mod 7)+1]: seq(A047565(n), n=0..100); # Wesley Ivan Hurt, Jul 21 2016
MATHEMATICA
LinearRecurrence[{1, 0, 0, 0, 0, 0, 1, -1}, {0, 1, 3, 4, 5, 6, 7, 8} , 50] (* G. C. Greubel, May 30 2016 *)
Select[Range[0, 200], MemberQ[{0, 1, 3, 4, 5, 6, 7}, Mod[#, 8] &]] (* Vincenzo Librandi, May 30 2016 *)
PROG
(Magma) [n: n in [0..150] | n mod 8 in [0, 1, 3, 4, 5, 6, 7]]; // Vincenzo Librandi, May 30 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved