A202674 Symmetric matrix based on (1,3,5,7,9,...), by antidiagonals.

1, 3, 3, 5, 10, 5, 7, 18, 18, 7, 9, 26, 35, 26, 9, 11, 34, 53, 53, 34, 11, 13, 42, 71, 84, 71, 42, 13, 15, 50, 89, 116, 116, 89, 50, 15, 17, 58, 107, 148, 165, 148, 107, 58, 17, 19, 66, 125, 180, 215, 215, 180, 125, 66, 19, 21, 74, 143, 212, 265, 286, 265, 212

Offset: 1

Author

Clark Kimberling, Dec 22 2011

Keywords

• nonn
• tabl

Comments

Let s=(1,3,5,7,9,...) 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 A202674 represents the matrix product M=T'*T. M is the self-fusion matrix of s, as defined at A193722. See A202675 for characteristic polynomials of principal submatrices of M.

...

row 1 (1,3,5,7,...) A005408

diagonal (1,10,35,84,...) A000447

antidiagonal sums (1,6,20,50,...) A002415

Examples

			Northwest corner:
1....3....5.....7.....9
3...10...18....26....34
5...18...35....53....71
7...26...53....84...116
9...34...71...116...165
		

Crossrefs

Cf. A005408, A202675, A193722.

Programs

Mathematica

U = NestList[Most[Prepend[#, 0]] &, #, Length[#] - 1] &[Table[2 k - 1, {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}]]