1,2

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.

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

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}]]

Cf. A203956, A202453.

Sequence in context: A368255 A368256 A185688 * A039638 A090926 A023503

Adjacent sequences: A203952 A203953 A203954 * A203956 A203957 A203958

nonn,tabl

Clark Kimberling, Jan 08 2012

approved