A086351 T(n,3) of A086350.

1, 4, 17, 74, 325, 1432, 6317, 27878, 123049, 543148, 2397545, 10583234, 46716589, 206216896, 910285253, 4018193246, 17737162705, 78295623508, 345613602113, 1525612248122, 6734378273941, 29726983906792, 131221255523165

Offset: 0

Author

Paul Barry, Jul 18 2003

Keywords

• easy
• nonn

Comments

Binomial transform of A007052. Second binomial transform of Pell numbers A000129 (without leading zero).

Links

• Index entries for linear recurrences with constant coefficients, signature (6,-7).

Programs

PARI

a(n)=my(sqrt2=quadgen(8)); simplify(((1+sqrt2)*(3+sqrt2)^n-(1-sqrt2)*(3-sqrt2)^n)/sqrt2^3) \\ Charles R Greathouse IV, Oct 24 2014

Formula

G.f.: (1-2x)/(1-6x+7x^2);

a(n)=((1+sqrt(2))(3+sqrt(2))^n-(1-sqrt(2))(3-sqrt(2))^n)/(sqrt(8)).

a(n) = A081179(n+1)-2*A081179(n). - R. J. Mathar, Dec 05 2022