A086351 Row T(n,3) of square array A086350.

1, 4, 17, 74, 325, 1432, 6317, 27878, 123049, 543148, 2397545, 10583234, 46716589, 206216896, 910285253, 4018193246, 17737162705, 78295623508, 345613602113, 1525612248122, 6734378273941, 29726983906792, 131221255523165, 579238645791446, 2556883086086521, 11286627995979004

Offset

0,2

Comments

Binomial transform of A007052.

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

Links

Table of n, a(n) for n=0..25.

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

Formula

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

E.g.f.: exp(3*x) * (2*cosh(sqrt(2)*x) + sqrt(2)*sinh(sqrt(2)*x)) / 2. - Amiram Eldar, Feb 03 2026

Mathematica

LinearRecurrence[{6, -7}, {1, 4}, 25] (* Amiram Eldar, Feb 03 2026 *)

Prog

(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

Crossrefs

Cf. A000129, A007052, A081179, A086350.

Sequence in context: A363541 A184700 A125586 * A049027 A026751 A227504

Adjacent sequences: A086348 A086349 A086350 * A086352 A086353 A086354

Keyword

easy,nonn

Author

Paul Barry, Jul 18 2003

Status

approved