Search: id:A069745
Results 1-1 of 1 results found.

%I A069745
%S A069745 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,
%T A069745 57,59,71,71,84,87,99,103,119,121,139,144,161,167,189,193,217,225,248,
%U A069745 257,286,293,324,336,366,379,416,427,467,483,522,540,586,602,652,674
%N A069745 Expansion of 1/((1-x^2)(1-x^3)(1-x^6)(1-x^7)(1-x^8)).
%C A069745 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 point-after-touchdown (TD+PAT), 8 points for a touchdown 
               followed by the 2-point-conversion (TD+2PC).
%C A069745 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 2-point-conversion 
               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).
%C A069745 Also number of (unordered) ways of making change for n cents with coins 
               of sizes 2, 3, 6, 7 and 8 cents.
%F A069745 G.f.: 1/((1-x^2)*(1-x^3)*(1-x^6)*(1-x^7)*(1-x^8))
%e A069745 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).
%o A069745 (PARI) a(n)=polcoeff(1/((1-x^2)*(1-x^3)*(1-x^6)*(1-x^7)*(1-x^8)+x*O(x^n)),
               n) for(n=0,100,print1(a(n),","))
%Y A069745 Cf. A069183.
%Y A069745 Sequence in context: A061901 A078822 A154392 this_sequence A112199 A145815 
               A059851
%Y A069745 Adjacent sequences: A069742 A069743 A069744 this_sequence A069746 A069747 
               A069748
%K A069745 nonn
%O A069745 0,7
%A A069745 Rick L. Shepherd (rshepherd2(AT)hotmail.com), Apr 21 2002

Search completed in 0.001 seconds