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A202876 Symmetric matrix based on A000071, by antidiagonals.

%I A202876 #6 Jul 12 2012 00:39:53
%S A202876 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 A202876 66,52,33,54,86,111,122,122,111,86,54,88,141,184,206,214,206,184,141,
%U A202876 88,143,230,302,342,362,362,342,302,230,143,232,374,493,562,602
%N A202876 Symmetric matrix based on A000071, by antidiagonals.
%C A202876 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 A202876 Northwest corner:
%e A202876 1....2....4....7....12....20
%e A202876 2....5....10...18...31....52
%e A202876 4....10...21...38...66....111
%e A202876 7....18...38...70...122...206
%e A202876 12...31...66...122..214...362
%t A202876 s[k_] := -1 + Fibonacci[k + 2];
%t A202876 U = NestList[Most[Prepend[#, 0]] &, #, Length[#] - 1] &[Table[s[k], {k, 1, 15}]];
%t A202876 L = Transpose[U]; M = L.U; TableForm[M]
%t A202876 m[i_, j_] := M[[i]][[j]];
%t A202876 Flatten[Table[m[i, n + 1 - i], {n, 1, 12}, {i, 1, n}]]
%t A202876 f[n_] := Sum[m[i, n], {i, 1, n}] + Sum[m[n, j], {j, 1, n - 1}]
%t A202876 Table[f[n], {n, 1, 12}]
%t A202876 Table[Sqrt[f[n]], {n, 1, 12}]  (* A001924 *)
%t A202876 Table[m[1, j], {j, 1, 12}]     (* A000071 *)
%t A202876 Table[m[j, j], {j, 1, 12}]     (* A202462 *)
%Y A202876 Cf. A202877, A202876.
%K A202876 nonn,tabl
%O A202876 1,2
%A A202876 _Clark Kimberling_, Dec 26 2011