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A203955
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Symmetric matrix based on (1,2,3,1,2,3,1,2,3...), by antidiagonals.
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3
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1, 2, 2, 3, 5, 3, 1, 8, 8, 1, 2, 5, 14, 5, 2, 3, 5, 11, 11, 5, 3, 1, 8, 11, 15, 11, 8, 1, 2, 5, 14, 13, 13, 14, 5, 2, 3, 5, 11, 14, 19, 14, 11, 5, 3, 1, 8, 11, 15, 19, 19, 15, 11, 8, 1, 2, 5, 14, 13, 16, 28, 16, 13, 14, 5, 2, 3, 5, 11, 14, 19, 22, 22, 19, 14, 11, 5, 3, 1, 8
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OFFSET
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1,2
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COMMENTS
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Let s be the periodic sequence (1,2,3,1,2,3,...) 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 A203955 represents the matrix product M=T'*T. M is the self-fusion matrix of s, as defined at A193722. See A203956 for characteristic polynomials of principal submatrices of M, with interlacing zeros.
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LINKS
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EXAMPLE
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Northwest corner:
1....2....3....1....2....3
2....5....8....5....5....8
3....8....14...11...11...14
1....5....11...15...13...14
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MATHEMATICA
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t = {1, 2, 3}; t1 = Flatten[{t, 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] (* A203955 *)
m[i_, j_] := M[[i]][[j]];
Flatten[Table[m[i, n + 1 - i], {n, 1, 12}, {i, 1, n}]]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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