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

1,2

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

Links

Table of n, a(n) for n=1..63.

Example

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

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}]]

Crossrefs

Cf. A005408, A202675, A193722.

Sequence in context: A137202 A146926 A000198 * A027170 A132775 A174102

Adjacent sequences: A202671 A202672 A202673 * A202675 A202676 A202677

Keyword

nonn,tabl

Author

Clark Kimberling, Dec 22 2011

Status

approved