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

Author

Lee A. Newberg, Jun 01 2009

Keywords

• easy
• nonn

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

Examples

			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.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (0,1,1,0,0,1,1).

Crossrefs

A029150 gives the number of unordered ways to achieve a score of n.

Programs

PARI

lista(nn) = {x = xx + O(xx^nn); Vec(1/(1-x^2-x^3-x^6-x^7));} \\ Michel Marcus, Aug 13 2013

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