A069745 Expansion of 1/((1-x^2)(1-x^3)(1-x^6)(1-x^7)(1-x^8)).
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
Offset: 0
Examples
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).
Links
- Index entries for linear recurrences with constant coefficients, signature (0, 1, 1, 0, -1, 1, 1, 0, -2, -2, 0, 1, 0, -1, 0, 2, 2, 0, -1, -1, 1, 0, -1, -1, 0, 1).
Crossrefs
Cf. A069183.
Programs
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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),","))
Formula
G.f.: 1/((1-x^2)*(1-x^3)*(1-x^6)*(1-x^7)*(1-x^8))
Comments