A161939 a(n) = ((3+sqrt(2))*(4+sqrt(2))^n + (3-sqrt(2))*(4-sqrt(2))^n)/2.

3, 14, 70, 364, 1932, 10360, 55832, 301616, 1631280, 8827616, 47783008, 258677440, 1400457408, 7582175104, 41050997120, 222257525504, 1203346244352, 6515164597760, 35274469361152, 190983450520576, 1034025033108480

Offset: 0

Author

Al Hakanson (hawkuu(AT)gmail.com), Jun 22 2009

Keywords

• nonn

Comments

Fourth binomial transform of A162255.

Links

• Muniru A Asiru, Table of n, a(n) for n = 0..280
• Index entries for linear recurrences with constant coefficients, signature (8, -14).

Crossrefs

Cf. A162255, A161940 (Fifth binomial transform of A162255).

Programs

GAP

a := [3, 14];; for n in [3..10^2] do a[n] := 8*a[n-1] - 14*a[n-2]; od; a; # Muniru A Asiru, Feb 02 2018

Magma

Z:=PolynomialRing(Integers()); N:=NumberField(x^2-2); S:=[ ((3+r)*(4+r)^n+(3-r)*(4-r)^n)/2: n in [0..20] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 01 2009

Maple

seq(simplify(((3+sqrt(2))*(4+sqrt(2))^n+(3-sqrt(2))*(4-sqrt(2))^n)*1/2), n = 0 .. 20); # Emeric Deutsch, Jun 28 2009

Mathematica

LinearRecurrence[{8,-14},{3,14},30] (* Harvey P. Dale, May 10 2012 *)

PARI

x='x+O('x^30); Vec((3-10*x)/(1-8*x+14*x^2)) \\ G. C. Greubel, Aug 17 2018

Formula

a(n) = 8*a(n-1) - 14*a(n-2) for n > 1; a(0) = 3; a(1) = 14.

G.f.: (3-10*x)/(1-8*x+14*x^2).

Extensions

Definition corrected by Emeric Deutsch, Jun 28 2009

Edited and extended beyond a(5) by Klaus Brockhaus, Jul 01 2009

Extended by Emeric Deutsch, Jun 28 2009