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 A122947 Triangular sequence: 1, 1 - x, -1 - x + x^2, 1 + 3 x + x^2 - x^3, 1 - x - 4 x^2 - x^3 +x^4, -1 - x + 6 x^2 + 8 x^3 + x^4 - x^5, -1 + 3 x + 6 x^2 - 7 x^3 - 10 x^4 - x^5 + x^6. 2

%I #6 Jun 03 2023 06:32:13

%S 1,1,-1,-1,-1,1,1,3,1,-1,1,-1,-4,-1,1,-1,-1,6,8,1,-1,-1,3,6,-7,-10,-1,

%T 1,-1,7,-6,-14,8,12,1,-1,1,1,-13,8,20,-8,-13,-1,1,-1,-3,11,17,-36,-26,

%U 27,21,1,-1,-1,1,19,-26,-53,63,53,-32,-25,-1,1,-1,5,15,-89,54,144,-102,-92,37,29,1,-1,1,3,-27,-10,169,-89,-226,127,121

%N Triangular sequence: 1, 1 - x, -1 - x + x^2, 1 + 3 x + x^2 - x^3, 1 - x - 4 x^2 - x^3 +x^4, -1 - x + 6 x^2 + 8 x^3 + x^4 - x^5, -1 + 3 x + 6 x^2 - 7 x^3 - 10 x^4 - x^5 + x^6.

%C Matrices: 1

%C X 1 {{1}}

%C 2 X 2 {{1, 1}, {1, 0}}

%C 3 X 3 {{1, 1, 1}, {1, 0, 1}, {1, 1, 0}}

%C 4 X 4 {{1, 1, 1, 1}, {1, 0, 1, 0}, {1, 1, 0, 0}, {1, 0, 0, 0}}

%C 5 X 5 {{1, 1, 1, 1, 1}, {1, 0, 1, 0, 1}, {1, 1, 0, 0, 1}, {1, 0, 0, 0, 1}, {1, 1, 1, 1, 0}}

%C 6 X 6 {{1, 1, 1, 1, 1, 1}, {1, 0, 1, 0, 1, 0}, {1, 1, 0, 0, 1, 1}, {1, 0, 0, 0, 1, 0}, {1, 1, 1, 1, 0, 0}, {1, 0, 1, 0, 0, 0}}

%e Triangle sequence:

%e {1},

%e {1, -1},

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

%e {1, 3, 1, -1},

%e {1, -1, -4, -1, 1},

%e {-1, -1, 6, 8, 1, -1},

%e {-1, 3, 6, -7, -10, -1, 1},

%e {-1, 7, -6, -14, 8, 12, 1, -1}

%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, 0], {n, 0, d - 1}, {m, 0, d - 1}]; Join[{{1}},

%t Table[CoefficientList[CharacteristicPolynomial[An[d], x], x], {d,1, 20}]];

%t Flatten[%]

%K tabl,uned,less,sign

%O 1,8

%A _Roger L. Bagula_ and _Gary W. Adamson_, Oct 24 2006

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Last modified May 29 20:46 EDT 2024. Contains 372952 sequences. (Running on oeis4.)