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A202676
Symmetric matrix based on (1,4,7,10,13,...), by antidiagonals.
3
1, 4, 4, 7, 17, 7, 10, 32, 32, 10, 13, 47, 66, 47, 13, 16, 62, 102, 102, 62, 16, 19, 77, 138, 166, 138, 77, 19, 22, 92, 174, 232, 232, 174, 92, 22, 25, 107, 210, 298, 335, 298, 210, 107, 25, 28, 122, 246, 364, 440, 440, 364, 246, 122, 28, 31, 137, 282, 430
OFFSET
1,2
COMMENTS
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.
...
row 1 (1,4,7,10,...) A016777
diagonal (1,17,66,166,...) A024215
...
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).
EXAMPLE
Northwest corner:
1....4....7...10...13...16
4...17...32...47...62...77
7...32...66..102..138..174
10..47..102..166..232..298
13..62..138..232..335..440
MATHEMATICA
U = NestList[Most[Prepend[#, 0]] &, #, Length[#] - 1] &[Table[3 k - 2, {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}]]
CROSSREFS
Cf. A202677.
Sequence in context: A323657 A238389 A115292 * A330765 A336718 A173324
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Dec 22 2011
STATUS
approved