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
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
Comments