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Symmetric matrix based on (1,2,3,1,2,3,1,2,3...), by antidiagonals.
3

%I #6 Jul 12 2012 00:39:54

%S 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,

%T 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,

%U 13,16,28,16,13,14,5,2,3,5,11,14,19,22,22,19,14,11,5,3,1,8

%N Symmetric matrix based on (1,2,3,1,2,3,1,2,3...), by antidiagonals.

%C 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.

%e Northwest corner:

%e 1....2....3....1....2....3

%e 2....5....8....5....5....8

%e 3....8....14...11...11...14

%e 1....5....11...15...13...14

%t t = {1, 2, 3}; t1 = Flatten[{t, t, t, t, t, t, t, t, t}];

%t s[k_] := t1[[k]];

%t U = NestList[Most[Prepend[#, 0]] &, #, Length[#] - 1] &[

%t Table[s[k], {k, 1, 15}]];

%t L = Transpose[U]; M = L.U; TableForm[M] (* A203955 *)

%t m[i_, j_] := M[[i]][[j]];

%t Flatten[Table[m[i, n + 1 - i], {n, 1, 12}, {i, 1, n}]]

%Y Cf. A203956, A202453.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Jan 08 2012