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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 (list; graph; refs; listen; history; text; internal format)
 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 LINKS Index entries for linear recurrences with constant coefficients, signature (0,1,1,0,0,1,1). 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 Adjacent sequences:  A160990 A160991 A160992 * A160994 A160995 A160996 KEYWORD easy,nonn AUTHOR Lee A. Newberg, Jun 01 2009 STATUS approved

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Last modified October 14 09:25 EDT 2019. Contains 327995 sequences. (Running on oeis4.)