A202869 - OEIS

%I #9 Oct 24 2024 05:40:24

%S 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,

%T 35,11,12,42,66,87,87,66,42,12,14,47,79,108,126,108,79,47,14,16,54,90,

%U 132,159,159,132,90,54,16,17,62,103,151,196,207,196,151,103,62

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

%C 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.

%e Northwest corner:

%e 1...3....4....6....8....9

%e 3...10...15...22...30...35

%e 4...15...26...39...54...66

%e 6...22...39...62...87...108

%e 8...30...54...87...126..159

%t s[k_] := Floor[k*GoldenRatio];

%t U = NestList[Most[Prepend[#, 0]] &, #, Length[#] - 1] &[Table[s[k], {k, 1, 15}]];

%t L = Transpose[U]; M = L.U; TableForm[M]

%t m[i_, j_] := M[[i]][[j]];

%t Flatten[Table[m[i, n + 1 - i], {n, 1, 12}, {i, 1, n}]]

%t f[n_] := Sum[m[i, n], {i, 1, n}] + Sum[m[n, j], {j, 1, n - 1}]

%t Table[f[n], {n, 1, 12}]

%t Table[Sqrt[f[n]], {n, 1, 12}]   (* A054347 *)

%t Table[m[1, j], {j, 1, 12}]        (* A000201 *)

%Y Cf. A202870.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Dec 26 2011