This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A203951 Symmetric matrix based on (1,0,0,0,1,0,0,0,...), by antidiagonals. 4
 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 0, 2, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,41 COMMENTS Let s be the periodic sequence (1,0,0,0,1,0,0,0,...) and let T be the infinite square matrix whose n-th row is formed by putting n-1 zeros before the terms of s.  Let T' be the transpose of T.  Then A203951 represents the matrix product M=T'*T.  M is the self-fusion matrix of s, as defined at A193722.  See A203952 for characteristic polynomials of principal submatrices of M, with interlacing zeros. LINKS EXAMPLE Northwest corner: 1 0 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 2 0 0 0 2 0 0 1 0 0 0 2 0 0 0 2 0 0 1 0 0 0 2 0 0 0 0 0 0 1 0 0 0 2 0 0 1 0 0 0 2 0 0 0 3 0 MATHEMATICA t = {1, 0, 0, 0}; t1 = Flatten[{t, t, t, t, t, t, t, t}]; f[k_] := t1[[k]]; U[n_] :=   NestList[Most[Prepend[#, 0]] &, #, Length[#] - 1] &[    Table[f[k], {k, 1, n}]]; L[n_] := Transpose[U[n]]; p[n_] := CharacteristicPolynomial[L[n].U[n], x]; c[n_] := CoefficientList[p[n], x] TableForm[Flatten[Table[p[n], {n, 1, 10}]]] Table[c[n], {n, 1, 12}] Flatten[%]  (* A203952 *) CROSSREFS Cf. A203951, A202453. Sequence in context: A111594 A322549 A237996 * A323591 A105348 A016406 Adjacent sequences:  A203948 A203949 A203950 * A203952 A203953 A203954 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Jan 08 2012 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 October 21 20:44 EDT 2019. Contains 328315 sequences. (Running on oeis4.)