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A203003 Symmetric matrix based on A007598(n+1), by antidiagonals. 3
1, 4, 4, 9, 17, 9, 25, 40, 40, 25, 64, 109, 98, 109, 64, 169, 281, 265, 265, 281, 169, 441, 740, 685, 723, 685, 740, 441, 1156, 1933, 1802, 1865, 1865, 1802, 1933, 1156, 3025, 5065, 4709, 4910, 4819, 4910, 4709, 5065, 3025, 7921, 13256, 12337, 12827 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Let s=A007598(n+1) (squared Fibonacci numbers, beginning with F(2)), 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 A203003 represents the matrix product M=T'*T.  M is the self-fusion matrix of s, as defined at A193722.  See A203004 for characteristic polynomials of principal submatrices of M, with interlacing zeros.

LINKS

Table of n, a(n) for n=1..49.

EXAMPLE

Northwest corner:

1....4.....9....25....64

4....17....40...109...281

9....40....98...265...685

25...109...265..1865

MATHEMATICA

s[k_] := Fibonacci[k + 1]^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]];  (* A203003 *)

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}]    (* A119996 *)

Table[m[1, j], {j, 1, 12}]       (* A007598(n+1) *)

CROSSREFS

Cf. A203004, A203001, A202453.

Sequence in context: A061886 A059815 A202670 * A319646 A214826 A135065

Adjacent sequences:  A203000 A203001 A203002 * A203004 A203005 A203006

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Dec 27 2011

STATUS

approved

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Last modified November 14 22:17 EST 2019. Contains 329134 sequences. (Running on oeis4.)