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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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Let s=(1,3,4,6,8,...)=A000201) 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 A202869 represents the matrix product M=T'*T.  M is the self-fusion 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

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Last modified April 24 13:28 EDT 2014. Contains 240983 sequences.