OFFSET
0,5
COMMENTS
Equivalently, a(n) is the number of compositions of n with odd-indexed parts being 1 and even-indexed parts being between 2 and 7. - Andrew Howroyd, Jan 14 2020
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,1,1,1,1,1,1).
FORMULA
a(n) = a(n-3) + a(n-4) + a(n-5) + a(n-6) + a(n-7) + a(n-8) for n >= 8.
G.f.: (1 + x)/(1 - x^3 - x^4 - x^5 - x^6 - x^7 - x^8). - Andrew Howroyd, Jan 14 2020
EXAMPLE
For n=0 there is one way to score zero points - pot nothing, potting a single red is the one way to have a break of one, a break of two is impossible (as defined here), a break of three can only be achieved with a red followed by a yellow, ...
PROG
(PARI) Vec((1 + x)/(1 - x^3 - x^4 - x^5 - x^6 - x^7 - x^8) + O(x^50)) \\ Andrew Howroyd, Jan 14 2020
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Rob Cummings (robc(AT)rocoto.demon.co.uk), Aug 14 2010
STATUS
approved