A160993 The number of ordered ways to achieve a score of n in American football.

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

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)*(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