A202869 - OEIS

A202869

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

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 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}]];