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A203953 Symmetric matrix based on (1,2,1,2,1,2,...), by antidiagonals. 3
1, 2, 2, 1, 5, 1, 2, 4, 4, 2, 1, 5, 6, 5, 1, 2, 4, 6, 6, 4, 2, 1, 5, 6, 10, 6, 5, 1, 2, 4, 6, 8, 8, 6, 4, 2, 1, 5, 6, 10, 11, 10, 6, 5, 1, 2, 4, 6, 8, 10, 10, 8, 6, 4, 2, 1, 5, 6, 10, 11, 15, 11, 10, 6, 5, 1, 2, 4, 6, 8, 10, 12, 12, 10, 8, 6, 4, 2, 1, 5, 6, 10, 11, 15, 16, 15, 11, 10 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Let s be the periodic sequence (1,2,1,2,1,2,...) 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 A203951 represents the matrix product M=T'*T.  M is the self-fusion matrix of s, as defined at A193722.  See A203954 for characteristic polynomials of principal submatrices of M, with interlacing zeros.

LINKS

Table of n, a(n) for n=1..88.

EXAMPLE

Northwest corner:

1 2 1 2 1 2 1

2 5 4 5 4 5 4

1 3 6 6 6 6 6

MATHEMATICA

t = {1, 2}; t1 = Flatten[{t, 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]  (* A203953 *)

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

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

CROSSREFS

Cf. A203954, A202453.

Sequence in context: A192456 A226948 A010243 * A326933 A123398 A277495

Adjacent sequences:  A203950 A203951 A203952 * A203954 A203955 A203956

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Jan 08 2012

STATUS

approved

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Last modified November 14 17:24 EST 2019. Contains 329126 sequences. (Running on oeis4.)