

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
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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 nth row is formed by putting n1 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 selffusion 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



