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A158418 A triangle sequence from matrix polynomials of a three symbol type {0, 1, 2}: 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, 2, 0]], {n, 0, d - 1}, {m, 0, d - 1}]. 0

%I

%S 1,1,-1,1,-3,1,1,-5,5,-1,-3,11,-4,-5,1,-3,17,-18,-2,7,-1,9,-39,12,35,

%T -12,-7,1,-27,81,54,-104,-28,30,7,-1,-135,621,-459,-286,266,58,-43,-7,

%U 1,-135,891,-1269,155,652,-216,-119,37,9,-1,405,-2133,1431,1986,-1677

%N A triangle sequence from matrix polynomials of a three symbol type {0, 1, 2}: 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, 2, 0]], {n, 0, d - 1}, {m, 0, d - 1}].

%C Row sums are:

%C {1, 2, 5, 12, 24, 48, 115, 332, 1876, 3484, 8969,...}.

%C Example matrix:

%C M(4)={{1, 1, 1, 1},

%C {1, 2, 1, 2},

%C {1, 1, 2, 2},

%C {1, 2, 2, 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, 2, 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 {1, -3, 1},

%e {1, -5, 5, -1},

%e {-3, 11, -4, -5, 1},

%e {-3, 17, -18, -2, 7, -1},

%e {9, -39, 12, 35, -12, -7, 1},

%e {-27, 81, 54, -104, -28, 30, 7, -1},

%e {-135, 621, -459, -286, 266, 58, -43, -7, 1},

%e {-135, 891, -1269, 155, 652, -216, -119, 37, 9, -1},

%e {405, -2133, 1431, 1986, -1677, -621, 543, 102, -61, -9, 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, 2, 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 0,5

%A _Roger L. Bagula_, Mar 18 2009

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Last modified October 3 02:59 EDT 2022. Contains 357230 sequences. (Running on oeis4.)