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

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1664

Wikipedia, Minor (linear algebra)

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

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 *)

Crossrefs

Column k=2 of A184173.

Cf. A007318, A369906.

Sequence in context: A005023 A094256 A094891 * A192803 A052161 A080960

Adjacent sequences: A306373 A306374 A306375 * A306377 A306378 A306379

Keyword

nonn

Author

Alois P. Heinz, Feb 11 2019

Status

approved