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A122947 Binary Hadamard Matrix self-Similarity of the Pascal triangle type used to give characteristic polynomials as a 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
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, 1, -1, 7, -6, -14, 8, 12, 1, -1, 1, 1, -13, 8, 20, -8, -13, -1, 1, -1, -3, 11, 17, -36, -26, 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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,8

COMMENTS

Matrices: 1 X 1 {{1}} 2 X 2 {{1, 1}, {1, 0}} 3 X 3 {{1, 1, 1}, {1, 0, 1}, {1, 1, 0}} 4 X 4 {{1, 1, 1, 1}, {1, 0, 1, 0}, {1, 1, 0, 0}, {1, 0, 0, 0}} 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}} 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}}

LINKS

Table of n, a(n) for n=1..87.

FORMULA

c(i,k)=Floor[Mod[i/2^k,2]] a(i,j)=If[Sum[c(i,k)*c(j,k),{k,0,d-1}]==0,1,0] a(i,j)->p(n,x) p(n,x)->{t(n,m)

EXAMPLE

Triangle sequence:

{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, 1},

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

MATHEMATICA

Clear[b, c, An] c[i_, k_] := Floor[Mod[i/2^k, 2]]; 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}}, Table[CoefficientList[CharacteristicPolynomial[An[d], x], x], {d, 1, 20}]]; Flatten[%]

CROSSREFS

Sequence in context: A268523 A195768 A016465 * A231147 A046534 A224489

Adjacent sequences:  A122944 A122945 A122946 * A122948 A122949 A122950

KEYWORD

tabl,uned,sign

AUTHOR

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

STATUS

approved

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Last modified September 20 12:42 EDT 2019. Contains 327237 sequences. (Running on oeis4.)