The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A124036 Alternating ones and twos tridiagonal matrices ( columns of 1's and twos) to give a triangular sequence: m(n,m,d)=If[ n == m, 1 + (1 - (-1)^(n + 1))/2, If[n == m - 1 || n == m + 1, 1 + (1 - (-1)^n)/2, 0]]. 0
 1, 1, -1, 0, -3, 1, -2, -1, 4, -1, -4, 6, 7, -6, 1, 0, 12, -7, -11, 7, -1, 8, 12, -40, -3, 23, -9, 1, 8, -20, -38, 59, 12, -30, 10, -1, 0, -72, 24, 162, -81, -54, 48, -12, 1, -16, -32, 172, 20, -267, 87, 82, -58, 13, -1, -32, 96, 328, -456, -392, 549, -19, -174, 82, -15, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Matrices: {{1}}, {{1, 2}, {1, 2}}, {{1, 2,0}, {1, 2, 1}, {0, 2, 1}}, {{1, 2, 0, 0}, {1, 2, 1, 0}, {0, 2, 1, 2}, {0, 0, 1, 2}}, {{1, 2, 0, 0, 0}, {1, 2, 1, 0,0}, {0, 2, 1, 2, 0}, {0, 0,1, 2, 1}, {0, 0, 0, 2, 1}}, {{1, 2, 0, 0, 0, 0}, {1, 2, 1, 0, 0, 0}, {0, 2,1, 2, 0, 0}, {0, 0, 1, 2, 1, 0}, {0, 0, 0, 2, 1, 2}, {0, 0, 0, 0, 1, 2}} Large roots: Table[x /. NSolve[Det[M[d] - x*IdentityMatrix[d]] == 0, x][[d]], {d, 1, 10}] {1., 3., 3.56155, 3.84224, 4., 4.09691, 4.16053, 4.20447, 4.23607, 4.25953} LINKS FORMULA m(n,m,d)=If[ n == m, 1 + (1 - (-1)^(n + 1))/2, If[n == m - 1 || n == m + 1, 1 + (1 - (-1)^n)/2, 0]] EXAMPLE Triangular sequence: {{1}}, {1, -1}, {0, -3, 1}, {-2, -1, 4, -1}, {-4, 6, 7, -6, 1}, {0, 12, -7, -11, 7, -1}, {8, 12, -40, -3, 23, -9, 1}, {8, -20, -38, 59, 12, -30, 10, -1}, {0, -72, 24, 162, -81, -54, 48, -12, 1}, {-16, -32, 172, 20, -267,87, 82, -58, 13, -1}, {-32, 96, 328, -456, -392, 549, -19, -174, 82, -15, 1} MATHEMATICA T[n_, m_, d_] := If[ n == m, 1 + ( 1 - (-1)^(n + 1))/2, If[n == m - 1 || n == m + 1, 1 + (1 - (-1)^n)/2, 0]] M[d_] := Table[T[n, m, d], {n, 1, d}, {m, 1, d}] Table[M[d], {d, 1, 10}] Table[Det[M[d]], {d, 1, 10}] Table[Det[M[d] - x*IdentityMatrix[d]], {d, 1, 10}] a = Join[{M[1]}, Table[CoefficientList[Det[M[d] - x*IdentityMatrix[d]], x], {d, 1, 10}]]; Flatten[a] MatrixForm[a] CROSSREFS Sequence in context: A191863 A166866 A177343 * A182481 A066743 A257915 Adjacent sequences:  A124033 A124034 A124035 * A124037 A124038 A124039 KEYWORD uned,sign AUTHOR Gary W. Adamson and Roger L. Bagula, Nov 02 2006 STATUS approved

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

Last modified August 5 15:41 EDT 2021. Contains 346477 sequences. (Running on oeis4.)