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A202676 Symmetric matrix based on (1,4,7,10,13,...), by antidiagonals.

%I A202676 #6 Jul 12 2012 00:39:53
%S A202676 1,4,4,7,17,7,10,32,32,10,13,47,66,47,13,16,62,102,102,62,16,19,77,
%T A202676 138,166,138,77,19,22,92,174,232,232,174,92,22,25,107,210,298,335,298,
%U A202676 210,107,25,28,122,246,364,440,440,364,246,122,28,31,137,282,430
%N A202676 Symmetric matrix based on (1,4,7,10,13,...), by antidiagonals.
%C A202676 Let s=(1,4,7,10,13,...) 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 A202676 represents the matrix product M=T'*T.  M is the self-fusion matrix of s, as defined at A193722.  See A202677 for characteristic polynomials of principal submatrices of M.
%C A202676 ...
%C A202676 row 1 (1,4,7,10,...) A016777
%C A202676 diagonal (1,17,66,166,...) A024215
%C A202676 ...
%C A202676 Sum[m[i, n], {i, 1, n}] + Sum[m[n, j], {j, 1, n - 1}]: (1,25,144,484,..), the squares of the pentagonal numbers (A000326).
%e A202676 Northwest corner:
%e A202676 1....4....7...10...13...16
%e A202676 4...17...32...47...62...77
%e A202676 7...32...66..102..138..174
%e A202676 10..47..102..166..232..298
%e A202676 13..62..138..232..335..440
%t A202676 U = NestList[Most[Prepend[#, 0]] &, #, Length[#] - 1] &[Table[3 k - 2, {k, 1, 15}]];
%t A202676 L = Transpose[U]; M = L.U; TableForm[M]
%t A202676 m[i_, j_] := M[[i]][[j]];
%t A202676 Flatten[Table[m[i, n + 1 - i], {n, 1, 12}, {i, 1, n}]]
%Y A202676 Cf. A202677.
%K A202676 nonn,tabl
%O A202676 1,2
%A A202676 _Clark Kimberling_, Dec 22 2011