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 A203945 Symmetric matrix based on (1,0,0,1,0,0,1,0,0,...), by antidiagonals. 3
 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 3, 0, 0, 2, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,25 COMMENTS Let s be the periodic sequence (1,0,0,1,0,0,...)  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 A203945 represents the matrix product M=T'*T.  M is the self-fusion matrix of s, as defined at A193722.  See A203946 for characteristic polynomials of principal submatrices of M, with interlacing zeros. LINKS EXAMPLE Northwest corner: 1...0...0...1...0...0...1 0...1...0...0...1...0...0 0...0...1...0...0...1...0 1...0...0...2...0...0...2 0...1...0...0...2...0...0 MATHEMATICA t = {1, 0, 0}; t1 = Flatten[{t, t, t, t, t, t, t, t}]; s[k_] := t1[[k]]; U = NestList[Most[Prepend[#, 0]] &, #, Length[#] - 1] &[    Table[s[k], {k, 1, 15}]]; L = Transpose[U]; M = L.U; TableForm[M] m[i_, j_] := M[[i]][[j]]; Flatten[Table[m[i, n + 1 - i], {n, 1, 12}, {i, 1, n}]] CROSSREFS Cf. A203946, A202453. Sequence in context: A057918 A242192 A016380 * A212663 A015692 A016232 Adjacent sequences:  A203942 A203943 A203944 * A203946 A203947 A203948 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Jan 08 2012 STATUS approved

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Last modified December 12 17:33 EST 2019. Contains 329960 sequences. (Running on oeis4.)