

A202869


Symmetric matrix based on the lower Wythoff sequence, A000201, by antidiagonals.


3



1, 3, 3, 4, 10, 4, 6, 15, 15, 6, 8, 22, 26, 22, 8, 9, 30, 39, 39, 30, 9, 11, 35, 54, 62, 54, 35, 11, 12, 42, 66, 87, 87, 66, 42, 12, 14, 47, 79, 108, 126, 108, 79, 47, 14, 16, 54, 90, 132, 159, 159, 132, 90, 54, 16, 17, 62, 103, 151, 196, 207, 196, 151, 103, 62
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OFFSET

1,2


COMMENTS

Let s=(1,3,4,6,8,...)=A000201) 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 A202869 represents the matrix product M=T'*T. M is the selffusion matrix of s, as defined at A193722. See A202870 for characteristic polynomials of principal submatrices of M,with interlacing zeros.


LINKS

Table of n, a(n) for n=1..65.


EXAMPLE

Northwest corner:
1...3....4....6....8....9
3...10...15...22...30...35
4...15...26...39...54...66
6...22...39...62...87...108
8...30...54...87...126..159


MATHEMATICA

s[k_] := Floor[k*GoldenRatio];
U = NestList[Most[Prepend[#, 0]] &, #, Length[#]  1] &[Table[s[k], {k, 1, 15}]];
L = Transpose[U]; M = L.U; TableForm[M]
m[i_, j_] := M[[i]][[j]];
Flatten[Table[m[i, n + 1  i], {n, 1, 12}, {i, 1, n}]]
f[n_] := Sum[m[i, n], {i, 1, n}] + Sum[m[n, j], {j, 1, n  1}]
Table[f[n], {n, 1, 12}]
Table[Sqrt[f[n]], {n, 1, 12}] (* A054347 *)
Table[m[1, j], {j, 1, 12}] (* A000201 *)


CROSSREFS

Cf. A202870.
Sequence in context: A130626 A175796 A115284 * A202871 A144626 A033707
Adjacent sequences: A202866 A202867 A202868 * A202870 A202871 A202872


KEYWORD

nonn,tabl


AUTHOR

Clark Kimberling, Dec 26 2011


STATUS

approved



