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

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).

Links

Table of n, a(n) for n=1..59.

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

Adjacent sequences: A202673 A202674 A202675 * A202677 A202678 A202679

Keyword

nonn,tabl

Author

Clark Kimberling, Dec 22 2011

Status

approved