OFFSET
0,3
COMMENTS
The Berndt-type sequence number 8a for the argument 2Pi/9 (see A215829 for details).
From the recurrence relation for A215829 it can be proved that a(3*n+2) is divisible by 3, a(3*n) is congruent to 1 modulo 3, and a(3*n+1) is congruent to 2 modulo 3, which implies that a(3*n)+a(3*n+1) is divisible by 3.
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,0,-33,0,0,105,0,0,1).
FORMULA
G.f.: (3*x^8-11*x^7+35*x^6-30*x^5-26*x^4-22*x^3-9*x^2+x-1)/(x^9+105*x^6-33*x^3-1). [Colin Barker, Oct 28 2012]
EXAMPLE
We have a(6)+3*a(3)=400, while a(30)+3*a(3) is divisible by 1000.
MATHEMATICA
LinearRecurrence[{0, 0, -33, 0, 0, 105, 0, 0, 1}, {1, -1, 9, -11, 59, -267, 433, -2041, 9753}, 30] (* Harvey P. Dale, Nov 29 2013 *)
PROG
(Magma) i:=28; I:=[3, -3, 27]; A215829:=[m le 3 select I[m] else -3*Self(m-1)+9*Self(m-2)+3*Self(m-3): m in [1..i]]; [3^(-1-Floor((n-1)/3))*A215829[n]: n in [1..i]]; // Bruno Berselli, Oct 02 2012
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Roman Witula, Aug 24 2012
STATUS
approved