A203953 Symmetric matrix based on (1,2,1,2,1,2,...), by antidiagonals.

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

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: A226948 A010243 A332963 * A326933 A123398 A277495

Adjacent sequences: A203950 A203951 A203952 * A203954 A203955 A203956

Keyword

nonn,tabl

Author

Clark Kimberling, Jan 08 2012

Status

approved