A202876 - OEIS

%I #6 Jul 12 2012 00:39:53

%S 1,2,2,4,5,4,7,10,10,7,12,18,21,18,12,20,31,38,38,31,20,33,52,66,70,

%T 66,52,33,54,86,111,122,122,111,86,54,88,141,184,206,214,206,184,141,

%U 88,143,230,302,342,362,362,342,302,230,143,232,374,493,562,602

%N Symmetric matrix based on A000071, by antidiagonals.

%C Let s=A000071 (Fibonacci numbers -1), 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 A202876 represents the matrix product M=T'*T.  M is the self-fusion matrix of s, as defined at A193722.  See A202877 for characteristic polynomials of principal submatrices of M, with interlacing zeros.

%e Northwest corner:

%e 1....2....4....7....12....20

%e 2....5....10...18...31....52

%e 4....10...21...38...66....111

%e 7....18...38...70...122...206

%e 12...31...66...122..214...362

%t s[k_] := -1 + Fibonacci[k + 2];

%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}]  (* A001924 *)

%t Table[m[1, j], {j, 1, 12}]     (* A000071 *)

%t Table[m[j, j], {j, 1, 12}]     (* A202462 *)

%Y Cf. A202877, A202876.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Dec 26 2011