

A180158


Number of ways are there to score a break of n points at snooker. Assuming an infinite number of reds are available, along with the usual six colors, and a break alternates redcolorred...


2



1, 1, 0, 1, 2, 2, 3, 5, 7, 9, 13, 20, 28, 39, 57, 82, 116, 166, 239, 342, 488, 699, 1002, 1433, 2050, 2936, 4203, 6014, 8608, 12323, 17638, 25244, 36134, 51722, 74030, 105961, 151669, 217091, 310729, 444760, 636607, 911202, 1304240, 1866817, 2672058, 3824629
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OFFSET

0,5


COMMENTS

Equivalently, a(n) is the number of compositions of n with oddindexed parts being 1 and evenindexed parts being between 2 and 7.  Andrew Howroyd, Jan 14 2020


LINKS



FORMULA

a(n) = a(n3) + a(n4) + a(n5) + a(n6) + a(n7) + a(n8) 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



