

A069745


Expansion of 1/((1x^2)(1x^3)(1x^6)(1x^7)(1x^8)).


1



1, 0, 1, 1, 1, 1, 3, 2, 4, 4, 5, 5, 8, 7, 11, 11, 14, 14, 19, 18, 24, 25, 30, 31, 39, 38, 47, 49, 57, 59, 71, 71, 84, 87, 99, 103, 119, 121, 139, 144, 161, 167, 189, 193, 217, 225, 248, 257, 286, 293, 324, 336, 366, 379, 416, 427, 467, 483, 522, 540, 586, 602, 652, 674
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OFFSET

0,7


COMMENTS

Number of ways for a team to score n points in American football, where, except as noted below, order of scoring does not matter. Points can be scored as follows: 2 points for a safety (S), 3 points for a field goal (FG), 6 points for a touchdown (TD), 7 points for a touchdown followed by the pointaftertouchdown (TD+PAT), 8 points for a touchdown followed by the 2pointconversion (TD+2PC).
Touchdowns, field goals and safeties are scored independently of each other. Note, though, that a lone point cannot be scored unless a touchdown has just been scored by the same team. Similarly, a 2pointconversion can only follow a touchdown. If these two restrictions were not part of the rules, then the U.S.A. football score sequence would be given instead by A069183 (with independent 1 and two independent types of 2s).
Also number of (unordered) ways of making change for n cents with coins of sizes 2, 3, 6, 7 and 8 cents.


LINKS

Table of n, a(n) for n=0..63.


FORMULA

G.f.: 1/((1x^2)*(1x^3)*(1x^6)*(1x^7)*(1x^8))


EXAMPLE

a(14)=11: Here are the 11 ways that 14 points can be scored (although some scenarios, especially involving safeties, are unlikely in actual games): TD+PAT+TD+PAT ((6+1)+(6+1)), TD+TD+S (6+6+2), TD+TD+2PC (6+(6+2)), TD+FG+FG+S (6+3+3+2), TD+2PC+FG+FG ((6+2)+3+3), TD+PAT+FG+S+S ((6+1)+3+2+2), TD+2PC+S+S+S ((6+2)+2+2+2), TD+S+S+S+S (6+2+2+2+2), FG+FG+FG+FG+S (3+3+3+3+2), FG+FG+S+S+S+S (3+3+2+2+2+2) and S+S+S+S+S+S+S (2+2+2+2+2+2+2).


PROG

(PARI) a(n)=polcoeff(1/((1x^2)*(1x^3)*(1x^6)*(1x^7)*(1x^8)+x*O(x^n)), n) for(n=0, 100, print1(a(n), ", "))


CROSSREFS

Cf. A069183.
Sequence in context: A078822 A224980 A154392 * A112199 A145815 A059851
Adjacent sequences: A069742 A069743 A069744 * A069746 A069747 A069748


KEYWORD

nonn,easy


AUTHOR

Rick L. Shepherd, Apr 21 2002


STATUS

approved



