A392840 a(n) is the permanent of the n X n matrix whose generic element is given by F(2*i-1)*L(2*i) if i = j and F(2*j)*L(2*j-1) if i != j with 1 <= i,j <= n, where F(n) = A000045(n) and L(n) = A000032(n).

1, 3, 54, 11372, 24402232, 470427113744, 76464199884839200, 100863678916460037730656, 1052225482021823728316486738880, 85200219091560225380744098751784469376, 52787384943336313613082514687962562095017999872, 247448834931151173143921914712695589420027507002927428608

Offset

0,2

Links

Table of n, a(n) for n=0..11.

Pedro Fernando Fernández Espinosa, Maritza Liliana Arciniegas Torres, and Camilo Andrés Acevedo Cadena, On Some Properties of Matrices with Entries Defined by Products of k-Fibonacci and k-Lucas Numbers, arXiv:2601.12644 [math.CO], 2026. See p. 6.

Example

a(3) = 11372:
  [3, 12, 88]
  [1, 14, 88]
  [1, 12, 90]

Mathematica

a[n_]:=Permanent[Table[If[i==j, Fibonacci[2i-1]LucasL[2i], Fibonacci[2j]LucasL[2j-1]], {i, n}, {j, n}]]; Join[{1}, Array[a, 12]]

Crossrefs

Cf. A000032, A000045, A001519, A001906, A005248,

Cf. A392837 (determinant), A392838 (trace), A392839 (eigenvalue of multiplicity 1).

Sequence in context: A156911 A214006 A154604 * A188798 A334248 A193256

Adjacent sequences: A392837 A392838 A392839 * A392841 A392842 A392843

Keyword

nonn

Author

Stefano Spezia, Jan 24 2026

Status

approved