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

Author

Clark Kimberling, Dec 22 2011

Keywords

• nonn
• tabl

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).

Examples

			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
		

Crossrefs

Cf. A202677.

Programs

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}]]