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A203955 Symmetric matrix based on (1,2,3,1,2,3,1,2,3...), by antidiagonals. 3
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..80.

EXAMPLE

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

MATHEMATICA

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}]]

CROSSREFS

Cf. A203956, A202453.

Sequence in context: A117918 A302495 A185688 * A039638 A090926 A023503

Adjacent sequences:  A203952 A203953 A203954 * A203956 A203957 A203958

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Jan 08 2012

STATUS

approved

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Last modified November 18 17:33 EST 2019. Contains 329287 sequences. (Running on oeis4.)