The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A158800 A characteristic polynomial triangle of a Hadamard matrix self-similar lower triangular system: H(2^(n-1)) -> H(2^n). 3
 1, -1, 0, 1, 1, 0, -2, 0, 1, 1, 0, -4, 0, 6, 0, -4, 0, 1, 1, 0, -8, 0, 28, 0, -56, 0, 70, 0, -56, 0, 28, 0, -8, 0, 1, 1, 0, -16, 0, 120, 0, -560, 0, 1820, 0, -4368, 0, 8008, 0, -11440, 0, 12870, 0, -11440, 0, 8008, 0, -4368, 0, 1820, 0, -560, 0, 120, 0, -16, 0, 1, 1, 0, -32, 0, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 COMMENTS Row sums are zero except for n=0. Example matrix: H(8)={{1, 0, 0, 0, 0, 0, 0, 0}, {1, -1, 0, 0, 0, 0, 0, 0}, {1, 0, -1, 0, 0, 0, 0, 0}, {1, -1, -1, 1, 0, 0, 0, 0}, {1, 0, 0, 0, -1, 0, 0, 0}, {1, -1, 0, 0, -1, 1, 0, 0}, {1, 0, -1, 0, -1, 0, 1, 0}, {1, -1, -1, 1, -1, 1, 1, -1}} H[2^n] * H[2^n] = IdentityMatrix[2^n] LINKS Table of n, a(n) for n=0..72. FORMULA Pattern Matrix: H(2) = {{1, 0}, {1, -1}} Iteration Matrix: m = {{1, 0}, {1, -1}} Matrix_Self_similar_Operator[H[2^(n-1)] = H(2^n). EXAMPLE {1}, {-1, 0, 1}, {1, 0, -2, 0, 1}, {1, 0, -4, 0, 6, 0, -4, 0, 1}, {1, 0, -8, 0, 28, 0, -56, 0, 70, 0, -56, 0, 28, 0, -8, 0, 1}, {1, 0, -16, 0, 120, 0, -560, 0, 1820, 0, -4368, 0, 8008, 0, -11440, 0, 12870, 0, -11440, 0, 8008, 0, -4368, 0, 1820, 0, -560, 0, 120, 0, -16, 0, 1}, {1, 0, -32, 0, 496, 0, -4960, 0, 35960, 0, -201376, 0, 906192, 0, -3365856, 0, 10518300, 0, -28048800, 0, 64512240, 0, -129024480, 0, 225792840, 0, -347373600, 0, 471435600, 0, -565722720, 0, 601080390, 0, -565722720, 0, 471435600, 0, -347373600, 0, 225792840, 0, -129024480, 0, 64512240, 0, -28048800, 0, 10518300, 0, -3365856, 0, 906192, 0, -201376, 0, 35960, 0, -4960, 0, 496, 0, -32, 0, 1} MATHEMATICA Clear[HadamardMatrix]; MatrixJoinH[A_, B_] := Transpose[Join[Transpose[A], Transpose[B]]]; KroneckerProduct[M_, N_] := Module[{M1, N1, LM, LN, N2}, M1 = M; N1 = N; LM = Length[M1]; LN = Length[N1]; Do[M1[[i, j]] = M1[[i, j]]N1, {i, 1, LM}, {j, 1, LM}]; Do[M1[[i, 1]] = MatrixJoinH[M1[[i, 1]], M1[[i, j]]], {j, 2, LM}, {i, 1, LM}]; N2 = {}; Do[AppendTo[N2, M1[[i, 1]]], {i, 1, LM}]; N2 = Flatten[N2]; Partition[N2, LM*LN, LM*LN]] HadamardMatrix[2] := {{1, 0}, {1, -1}}; HadamardMatrix[n_] := Module[{m}, m = {{1, 0}, {1, -1}}; KroneckerProduct[m, HadamardMatrix[n/2]]]; Table[HadamardMatrix[2^n], {n, 1, 4}]; Join[{{1}}, Table[CoefficientList[CharacteristicPolynomial[ HadamardMatrix[2^n], x], x], {n, 1, 6}]]; Flatten[%] CROSSREFS Sequence in context: A369816 A236541 A113206 * A144024 A185249 A075107 Adjacent sequences: A158797 A158798 A158799 * A158801 A158802 A158803 KEYWORD sign,tabf,uned AUTHOR Roger L. Bagula and Gary W. Adamson, Mar 27 2009 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 17 06:18 EDT 2024. Contains 373432 sequences. (Running on oeis4.)