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A122944 A nonsense sequence. 5

%I #14 Dec 18 2022 07:06:15

%S 1,1,-1,-1,-1,1,0,2,1,-1,1,-1,-4,-1,1,0,-2,2,6,1,-1,0,0,4,-2,-7,-1,1,

%T 0,2,-1,-9,3,9,1,-1,1,1,-13,8,20,-8,-13,-1,1,0,-2,-2,24,-15,-31,13,17,

%U 1,-1,0,0,4,4,-40,20,44,-14,-19,-1,1,0,0,0,-8,-4,56,-24,-54,14,20,1,-1,0,0,0,0,16,8,-88,30,71,-15,-22,-1,1,0,0,0,16,8

%N A nonsense sequence.

%H Roger Bagula and Gary Adamson, <a href="http://paulbourke.net/fractals/pascaltriangle/">Pascal's Triangle in Gray Code: its Hadamard and IFS</a>

%e Triangle:

%e {1},

%e {1, -1},

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

%e {0, 2, 1, -1},

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

%e {0, -2, 2,6, 1, -1},

%e {0, 0, 4, -2, -7, -1, 1},

%e {0, 2, -1, -9, 3, 9,1, -1},

%e {1, 1, -13, 8, 20, -8, -13, -1, 1},

%e {0, -2, -2, 24, -15, -31, 13,17, 1, -1},

%e {0, 0, 4, 4, -40, 20, 44, -14, -19, -1, 1},

%e {0, 0, 0, -8, -4, 56, -24, -54, 14, 20, 1, -1}

%e Polynomials:

%e 1,

%e 1 - x,

%e -1 - x + x^2,

%e 2 x + x^2 - x^3,

%e 1 - x - 4 x^2 - x^3 + x^4,

%e -2 x + 2 x^2 + 6 x^3 +x^4 - x^5,

%e 4 x^2 - 2 x^3 - 7 x^4 - x^5 +x^6,

%e 2 x - x^2 - 9 x^3 + 3 x^4 + 9 x^5 + x^6 - x^7

%t c[i_, k_] := Floor[Mod[i/2^k, 2]]; b[i_, k_] = If[c[i, k] == 0 && c[i, k + 1] == 0, 0, If[c[i, k] == 1 && c[i, k + 1] == 1, 0, 1]];

%t An[d_] := Table[If[Sum[b[n, k]*b[m, k], {k, 0, d - 1}] == 0, 1, 0], {n, 0, d - 1}, {m, 0, d - 1}]: a=Join[{{1}}, Table[CoefficientList[CharacteristicPolynomial[An[d], x], x], {d, 1, 20}]];

%t Flatten[a]

%t RowSum=Table[Apply[Plus, Abs[a[[n]]]], {n, 1, Length[a]}]

%Y Cf. A121801.

%K tabl,uned,sign

%O 1,8

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

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Last modified March 28 17:25 EDT 2024. Contains 371254 sequences. (Running on oeis4.)