A306376 Sum of the 2 X 2 minors in the n X n Pascal matrix.

0, 0, 1, 7, 34, 144, 574, 2226, 8533, 32587, 124453, 476145, 1826175, 7022379, 27072487, 104614863, 405122290, 1571859864, 6109296442, 23781666198, 92704406320, 361832294964, 1413879679672, 5530590849168, 21654384302110, 84859670743770, 332818903663390

Offset: 0

Author

Alois P. Heinz, Feb 11 2019

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1664
• Wikipedia, Minor (linear algebra)

Crossrefs

Column k=2 of A184173.

Cf. A007318, A369906.

Programs

Maple

a:= proc(n) option remember; `if`(n<3, (n-1)*n/2,
     ((7*n^2-16*n+6)*a(n-1)-2*(7*n^2-17*n+9)*a(n-2)+
      4*(n-1)*(2*n-3)*a(n-3))/(n*(n-2)))
    end:
seq(a(n), n=0..30);

Mathematica

a[n_] := a[n] = If[n < 3, (n-1)n/2,
     ((7n^2 - 16n + 6) a[n-1] - 2(7n^2 - 17n + 9) a[n-2] +
     4(n-1)(2n-3) a[n-3])/(n(n-2))];
a /@ Range[0, 30] (* Jean-François Alcover, May 03 2021, after Alois P. Heinz *)

Formula

G.f.: -1/(2*(x-1))*(1/(2*x-1)+1/sqrt(1-4*x)).

a(n) ~ 2^(2*n+1) / (3*sqrt(Pi*n)). - Vaclav Kotesovec, Feb 19 2024