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proposed

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.

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Let s=(1,3,4,6,8,...)=A000201) and let T be the infinite square matrix whose nth 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.

_Clark Kimberling (ck6(AT)evansville.edu), _, Dec 26 2011

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allocated for Clark KimberlingSymmetric 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

1,2

Let s=(1,3,4,6,8,...)=A000201) and let T be the infinite square matrix whose nth 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.

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

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 *)

Cf. A202870.

allocated

nonn,tabl

Clark Kimberling (ck6(AT)evansville.edu), Dec 26 2011

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editing

allocated for Clark Kimberling

allocated

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