A202876 Symmetric matrix based on A000071, by antidiagonals.

1, 2, 2, 4, 5, 4, 7, 10, 10, 7, 12, 18, 21, 18, 12, 20, 31, 38, 38, 31, 20, 33, 52, 66, 70, 66, 52, 33, 54, 86, 111, 122, 122, 111, 86, 54, 88, 141, 184, 206, 214, 206, 184, 141, 88, 143, 230, 302, 342, 362, 362, 342, 302, 230, 143, 232, 374, 493, 562, 602

Offset

1,2

Comments

Let s=A000071 (Fibonacci numbers -1), 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 A202876 represents the matrix product M=T'*T. M is the self-fusion matrix of s, as defined at A193722. See A202877 for characteristic polynomials of principal submatrices of M, with interlacing zeros.

Links

Table of n, a(n) for n=1..60.

Example

Northwest corner:
1....2....4....7....12....20
2....5....10...18...31....52
4....10...21...38...66....111
7....18...38...70...122...206
12...31...66...122..214...362

Mathematica

s[k_] := -1 + Fibonacci[k + 2];
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}]  (* A001924 *)
Table[m[1, j], {j, 1, 12}]     (* A000071 *)
Table[m[j, j], {j, 1, 12}]     (* A202462 *)

Crossrefs

Cf. A202877, A202876.

Sequence in context: A255368 A186101 A284722 * A128900 A136099 A210597

Adjacent sequences: A202873 A202874 A202875 * A202877 A202878 A202879

Keyword

nonn,tabl

Author

Clark Kimberling, Dec 26 2011

Status

approved