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A203001 Symmetric matrix based on A007598, by antidiagonals. 5
1, 1, 1, 4, 2, 4, 9, 5, 5, 9, 25, 13, 18, 13, 25, 64, 34, 41, 41, 34, 64, 169, 89, 113, 99, 113, 89, 169, 441, 233, 290, 266, 266, 290, 233, 441, 1156, 610, 765, 689, 724, 689, 765, 610, 1156, 3025, 1597, 1997, 1811, 1866, 1866, 1811, 1997, 1597, 3025 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Let s=A007598 (squared Fibonacci numbers), 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 A203001 represents the matrix product M=T'*T.  M is the self-fusion matrix of s, as defined at A193722.  See A203002 for characteristic polynomials of principal submatrices of M, with interlacing zeros.

LINKS

Table of n, a(n) for n=1..55.

EXAMPLE

Northwest corner:

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

1...2...5....13...34....89

4...5...18...41...113...290

9...13..41...99...266...724

MATHEMATICA

s[k_] := 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}]   (* A001654 *)

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

Table[m[2, j], {j, 1, 12}]      (* A001519 *)

Table[m[j, j], {j, 1, 12}]      (* A005969 *)

CROSSREFS

Cf. A203002, A202453.

Sequence in context: A007361 A128136 A048147 * A051666 A011382 A011302

Adjacent sequences:  A202998 A202999 A203000 * A203002 A203003 A203004

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Dec 27 2011

STATUS

approved

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Last modified November 20 02:34 EST 2019. Contains 329323 sequences. (Running on oeis4.)