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A306376
Sum of the 2 X 2 minors in the n X n Pascal matrix.
3
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
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.
Sequence in context: A005023 A094256 A094891 * A192803 A052161 A080960
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Feb 11 2019
STATUS
approved