login
A134815
Expansion of g.f. -x*(3*x^7+2*x^6+x^5+15*x^4+3*x^3-x^2+15*x-4)/((x^4+x-1)*(x^4+5*x-1)).
0
4, 9, 35, 162, 790, 3923, 19602, 98108, 491242, 2460009, 12319475, 61695247, 308967153, 1547295326, 7748795485, 38805671816, 194337325053, 973233918963, 4873918388052, 24408397608972, 122236325365629, 612154860741196, 3065648222085872, 15352649508027068, 76885483865485421, 385039574188146841
OFFSET
1,1
COMMENTS
Ratio is: 5.00796 Roots: three copies of the theta1 4b4 Pisot and new pisot NSolve[ -1 - 5 x^3 + x^4 == 0, x] {{x -> -0.564325}, {x -> 0.278181 - 0.525792I}, {x -> 0.278181 + 0.525792I]}, {x -> 5.00796}} Total game value: Det[M]/(Sum[Sum[If[i == j, M[[i, j]], 0], {i, 1, 16}], {j, 1, 16}] - Sum[Sum[If[i ==j, 0, M[[i, j]]], {i, 1, 16}], {j, 1, 16}])=-1/8 It seems possible that this kind of game cam be generalized to: Follower:Game_Value[MA]=1/(n-1) Leader:Game_Value[MB]=-1 Where the leader gets an (n+1) point payoff.
FORMULA
G.f.: -x*(3*x^7+2*x^6+x^5+15*x^4+3*x^3-x^2+15*x-4)/((x^4+x-1)*(x^4+5*x-1)). - Colin Barker, Nov 01 2012
CROSSREFS
Sequence in context: A182144 A182723 A176607 * A367992 A352002 A120073
KEYWORD
nonn,easy,less
AUTHOR
Roger L. Bagula, Jan 28 2008
EXTENSIONS
Meaningful name using given g.f. from Joerg Arndt, Oct 26 2024
STATUS
approved