

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
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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; twopoint conversion following a touchdown).  Bob Selcoe, Feb 16 2014


LINKS

Table of n, a(n) for n=0..40.
Index entries for linear recurrences with constant coefficients, signature (0,1,1,0,0,1,1).


FORMULA

G.f.: 1 / ( (1+x+x^2)*(1x^5+x^3x^2x) ).
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/(1x^2x^3x^6x^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
Adjacent sequences: A160990 A160991 A160992 * A160994 A160995 A160996


KEYWORD

easy,nonn


AUTHOR

Lee A. Newberg, Jun 01 2009


STATUS

approved



