

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



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



KEYWORD



AUTHOR



STATUS

approved



