A390679 a(n) is the permanent of the square matrix A(n) of order 2*n whose generic entry is A(i, j) = n*(2*i - (-1)^i - 3) + 2*j - (-1)^j/2 + (-1)^i - 3/2 with 1 <= i,j <= 2*n.

1, 2, 25456, 4237316640, 4641143801988096, 21554673989105266329600, 321725679938644429666942894080, 12776780124456086724647909301669888000, 1177656217569966231516887166301967113047244800, 227208414798817556276324254464686576989326580855603200, 84636938569466121967980317320556480770113134488834340290560000

Offset

0,2

Comments

Inspired by the matrices shown in Raptis link.

For n < 3 the matrix A(n) shows the Lebesgue Z-order curve pattern.

For n > 1, the matrix A(n) is singular.

Links

Table of n, a(n) for n=0..10.

Theophanes Raptis and Vasilios Raptis, Symmetries and Scale Invariance in Global Maps of Quantum Circuits, Proceedings 123, no. 1: 5 (2025). See p. 4.

Wikipedia, Z-order curve.

Example

a(1) = 2:
  [0, 1]
  [2, 3]
a(2) = 25456:
  [ 0,  1,  4,  5]
  [ 2,  3,  6,  7]
  [ 8,  9, 12, 13]
  [10, 11, 14, 15]
a(3) = 4237316640:
  [ 0,  1,  4,  5,  8,  9]
  [ 2,  3,  6,  7, 10, 11]
  [12, 13, 16, 17, 20, 21]
  [14, 15, 18, 19, 22, 23]
  [24, 25, 28, 29, 32, 33]
  [26, 27, 30, 31, 34, 35]

Mathematica

A[i_, j_, n_]:=n(2i-(-1)^i-3)+2j-(-1)^j/2+(-1)^i-3/2; a[n_]:=Permanent[Table[A[i, j, n], {i, 2n}, {j, 2n}]]; Join[{1}, Array[a, 10]]

Prog

(PARI) a(n) = matpermanent(matrix(2*n, 2*n, i, j, n*(2*i - (-1)^i - 3) + 2*j - (-1)^j/2 + (-1)^i - 3/2)); \\ Michel Marcus, Nov 15 2025

Crossrefs

Sequence in context: A132942 A237521 A131558 * A133857 A349519 A232869

Adjacent sequences: A390676 A390677 A390678 * A390680 A390681 A390682

Keyword

nonn

Author

Stefano Spezia, Nov 15 2025

Status

approved