A122944 A nonsense sequence.

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, 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, 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

Offset

1,8

Links

Table of n, a(n) for n=1..96.

Roger Bagula and Gary Adamson, Pascal's Triangle in Gray Code: its Hadamard and IFS

Example

Triangle:
  {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},
  {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, 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}
Polynomials:
  1,
  1 - x,
  -1 - x + x^2,
  2 x + x^2 - x^3,
  1 - x - 4 x^2 - x^3 + x^4,
  -2 x + 2 x^2 + 6 x^3 +x^4 - x^5,
  4 x^2 - 2 x^3 - 7 x^4 - x^5 +x^6,
  2 x - x^2 - 9 x^3 + 3 x^4 + 9 x^5 + x^6 - x^7

Mathematica

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]];
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}]];
Flatten[a]
RowSum=Table[Apply[Plus, Abs[a[[n]]]], {n, 1, Length[a]}]

Crossrefs

Cf. A121801.

Sequence in context: A118210 A061399 A161856 * A107688 A376267 A060097

Adjacent sequences: A122941 A122942 A122943 * A122945 A122946 A122947

Keyword

tabl,uned,sign

Author

Roger L. Bagula and Gary W. Adamson, Oct 24 2006

Status

approved