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A160993
The number of ordered ways to achieve a score of n in American football.
1
1, 0, 1, 1, 1, 2, 3, 4, 6, 9, 12, 18, 26, 37, 54, 78, 112, 162, 234, 337, 487, 703, 1014, 1464, 2113, 3049, 4401, 6352, 9167, 13231, 19096, 27560, 39777, 57409, 82856, 119584, 172592, 249096, 359513, 518874, 748874
OFFSET
0,6
COMMENTS
Number of compositions (ordered partitions) of n into parts 2, 3, 6, and 7. - Joerg Arndt, Aug 13 2013
The sequence holds only when considering number of points scored and not HOW those points are scored. Sequence A237997 applies when taking into account the two ways to score 2 points (safety; two-point conversion following a touchdown). - Bob Selcoe, Feb 16 2014
FORMULA
G.f.: 1 / ( (1+x+x^2)*(1-x^5+x^3-x^2-x) ).
a(n)+a(n+1)+a(n+2) = A107293(n+6). - R. J. Mathar, Feb 18 2014
EXAMPLE
There are four ways to get a total of 7 points: (a) touchdown and extra point, (b) a field goal followed by two safeties, (c) a safety, field goal, and safety, and (d) two safeties followed by a field goal.
PROG
(PARI) lista(nn) = {x = xx + O(xx^nn); Vec(1/(1-x^2-x^3-x^6-x^7)); } \\ Michel Marcus, Aug 13 2013
CROSSREFS
A029150 gives the number of unordered ways to achieve a score of n.
Sequence in context: A018669 A138857 A018130 * A171826 A000792 A018752
KEYWORD
easy,nonn
AUTHOR
Lee A. Newberg, Jun 01 2009
STATUS
approved