

A202873


Symmetric matrix based on (1,3,7,15,31,...), by antidiagonals.


3



1, 3, 3, 7, 10, 7, 15, 24, 24, 15, 31, 52, 59, 52, 31, 63, 108, 129, 129, 108, 63, 127, 220, 269, 284, 269, 220, 127, 255, 444, 549, 594, 594, 549, 444, 255, 511, 892, 1109, 1214, 1245, 1214, 1109, 892, 511, 1023, 1788, 2229, 2454, 2547, 2547, 2454
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OFFSET

1,2


COMMENTS

Let s=(1,3,7,15,31,...) 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 A202873 represents the matrix product M=T'*T. M is the selffusion matrix of s, as defined at A193722. See A202767 for characteristic polynomials of principal submatrices of M.


LINKS

Table of n, a(n) for n=1..52.


EXAMPLE

Northwest corner:
1.....3.....7...15...31.....63
3....10....24...52...108...220
7....24....59..129...269...549
15...52...129..284...594..1214
31...108..269..594..1245..2547


MATHEMATICA

s[k_] := 1 + 2^k;
U = NestList[Most[Prepend[#, 0]] &, #, Length[#]  1] &[Table[s[k], {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}]]
f[n_] := Sum[m[i, n], {i, 1, n}] + Sum[m[n, j], {j, 1, n  1}]
Table[f[n], {n, 1, 12}]
Table[Sqrt[f[n]], {n, 1, 12}] (* A000295, Eulerian *)
Table[m[1, j], {j, 1, 12}] (* A000225 *)
Table[m[2, j], {j, 1, 12}] (* A053208 *)


CROSSREFS

Cf. A202767.
Sequence in context: A117525 A075149 A161618 * A157933 A013915 A136445
Adjacent sequences: A202870 A202871 A202872 * A202874 A202875 A202876


KEYWORD

nonn,tabl


AUTHOR

Clark Kimberling, Dec 26 2011


STATUS

approved



