OFFSET
0,3
COMMENTS
This formula is considered in Theorem 5 of Shum's paper in References: on page 4 reads M(7^m,3) = (7^m - 2*m - 1)/4 for m >= 1, where M(r,s) is the number of the codewords in an optimal CAC(r,s), and CAC(r,s) denotes a conflict-avoiding codes of length r and weight s (see Introduction).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
K. W. Shum, On Conflict-Avoiding Codes of Weight Three and Odd Length, The Fifth International Workshop on Signal Design and Its Applications in Communications, October 10-14, 2011, Guilin, China.
Index entries for linear recurrences with constant coefficients, signature (9,-15,7).
FORMULA
G.f.: x*(1+2*x)/((1-7*x)*(1-x)^2).
a(n) = 9*a(n-1) - 15*a(n-2) + 7*a(n-3). - Robert Israel, Jul 09 2014
MATHEMATICA
Table[(7^n - 2 n - 1)/4, {n, 0, 30}] (* or *)
CoefficientList[Series[x (1 + 2 x)/((1 - 7 x) (1 - x)^2), {x, 0, 30}], x]
PROG
(Magma) [(7^n-2*n-1)/4: n in [0..25]];
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Jul 09 2014
EXTENSIONS
Edited by Bruno Berselli, Jul 09 2014
STATUS
approved