|
%I #2 Mar 30 2012 17:34:35
%S 1,1,-1,-2,0,1,4,4,-1,-1,12,-4,-7,1,1,-24,-16,18,10,-2,-1,-72,48,66,
%T -22,-15,2,1,-216,432,-54,-158,26,21,-2,-1,864,0,-864,128,230,-32,-25,
%U 2,1,-1728,-1728,1512,1328,-542,-318,73,31,-3,-1,-5184,1728,7992,-1968
%N A triangle sequence from matrix polynomials of a three symbol type {0, 1, -1}: c(i,k)= Floor[Mod[i/2^k, 2]]; M(d)=Table[If[Sum[c(n, k)*c(m, k), {k, 0, d - 1}] == 0, 1, If[Sum[c(n, k)*c(m, k), {k, 0, d - 1}] == 1, -1, 0]], {n, 0, d - 1}, {m, 0, d - 1}].
%C Row sums are:
%C {1, 2, 3, 10, 25, 71, 226, 910, 2146, 7264, 21842,...}.
%C Example matrix:
%C M(4)={{1, 1, 1, 1},
%C {1, -1, 1, -1},
%C {1, 1, -1, -1},
%C {1, -1, -1, 0}}.
%F c(i,k)= Floor[Mod[i/2^k, 2]];
%F m(d)=Table[If[Sum[c(n, k)*c(m, k), {k, 0, d - 1}] == 0, 1, If[Sum[c(n, k)*c(m, k), {k, 0, d - 1}] == 1, -1, 0]], {n, 0, d - 1}, {m, 0, d - 1}];
%F out_(n,m)=coefficient(characteristicpolynomial(M(n),x),x)
%e {1},
%e {1, -1},
%e {-2, 0, 1},
%e {4, 4, -1, -1},
%e {12, -4, -7, 1, 1},
%e {-24, -16, 18, 10, -2, -1},
%e {-72, 48, 66, -22, -15, 2, 1},
%e {-216, 432, -54, -158, 26, 21, -2, -1},
%e {864, 0, -864, 128, 230, -32, -25, 2, 1},
%e {-1728, -1728, 1512, 1328, -542, -318, 73, 31, -3, -1},
%e {-5184, 1728, 7992, -1968, -3522, 738, 579, -87, -40, 3, 1}
%t Clear[c, b, a, An];
%t c[i_, k_] := Floor[Mod[i/2^k, 2]];
%t An[d_] := Table[If[Sum[c[n, k]*c[m, k], {k, 0, d - 1}] == 0, 1, If[Sum[c[n, k]*c[m, k], {k, 0, d - 1}] == 1, -1, 0]], {n, 0, d - 1}, {m, 0, d - 1}];
%t Table[An[n], {n, 1, 10}];
%t a = Join[{{1}}, Table[CoefficientList[CharacteristicPolynomial[An[ d], x], x], {d, 1, 10}]] ;
%t Flatten[a]
%t RowSum = Table[Apply[Plus, Abs[a[[n]]]], {n, 1, Length[a]}];
%K sign,tabl,uned
%O 0,4
%A _Roger L. Bagula_, Mar 18 2009
|
