

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
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OFFSET

1,2


COMMENTS

Let s=(1,3,5,7,9,...) and let T be the infinite square matrix whose nth row is formed by putting n1 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 selffusion 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



