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A202674 Symmetric matrix based on (1,3,5,7,9,...), by antidiagonals. 3
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified November 15 11:18 EST 2019. Contains 329144 sequences. (Running on oeis4.)