A164034 a(n) = ((4+3*sqrt(2))*(4+sqrt(2))^n + (4-3*sqrt(2))*(4-sqrt(2))^n)/4.

2, 11, 60, 326, 1768, 9580, 51888, 280984, 1521440, 8237744, 44601792, 241485920, 1307462272, 7078895296, 38326690560, 207508990336, 1123498254848, 6082860174080, 32933905824768, 178311204161024, 965414951741440

Offset: 0

Author

Al Hakanson (hawkuu(AT)gmail.com), Aug 08 2009

Keywords

• nonn

Comments

Binomial transform of A164033. Fourth binomial transform of A164090. Inverse binomial transform of A164035.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (8,-14).

Crossrefs

Cf. A164033, A164090, A164035.

Programs

Magma

Z:= PolynomialRing(Integers()); N:=NumberField(x^2-2); S:=[ ((4+3*r)*(4+r)^n+(4-3*r)*(4-r)^n)/4: n in [0..20] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 09 2009

Mathematica

LinearRecurrence[{8,-14},{2,11},30] (* Harvey P. Dale, Aug 09 2016 *)

PARI

x='x+O('x^50); Vec((2-5*x)/(1-8*x+14*x^2)) \\ G. C. Greubel, Sep 08 2017

Formula

a(n) = 8*a(n-1) - 14*a(n-2) for n > 1; a(0) = 2, a(1) = 11.

G.f.: (2-5*x)/(1-8*x+14*x^2).

E.g.f.: (2*cosh(sqrt(2)*x) + (3*sqrt(2)/2)*sinh(sqrt(2)*x))*exp(4*x). - G. C. Greubel, Sep 08 2017

Extensions

Edited and extended beyond a(5) by Klaus Brockhaus, Aug 09 2009