A369906 Sum of the permanents of all 2 X 2 submatrices in the n X n Pascal matrix.

0, 0, 1, 9, 50, 234, 1016, 4256, 17509, 71349, 289223, 1168815, 4714425, 18991401, 76434373, 307411285, 1235697666, 4964876706, 19940653388, 80062371380, 321361753426, 1289589924226, 5173842730758, 20753408180790, 83231772855896, 333749033253560

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1661

Wikipedia, Permanent (mathematics)

Formula

a(n) ~ 4^n/3 * (1 - 1/sqrt(Pi*n)). - Vaclav Kotesovec, Feb 19 2024

Maple

a:= proc(n) option remember; `if`(n<5, [0, 0, 1, 9, 50][n+1],
      ((13*n-12)*a(n-1)-8*(8*n-15)*a(n-2)+4*(37*n-105)*
       a(n-3)-40*(4*n-15)*a(n-4)+32*(2*n-9)*a(n-5))/n)
    end:
seq(a(n), n=0..32);

Crossrefs

Column k=2 of A369559.

Cf. A007318, A306376 (same for determinants).

Sequence in context: A279979 A222993 A171480 * A257589 A341921 A231413

Adjacent sequences: A369903 A369904 A369905 * A369907 A369908 A369909

Keyword

nonn

Author

Alois P. Heinz, Feb 05 2024

Status

approved