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

0,1

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).

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).

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 *)

Prog

(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=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
(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
(PARI) x='x+O('x^30); Vec((3-10*x)/(1-8*x+14*x^2)) \\ G. C. Greubel, Aug 17 2018

Crossrefs

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

Sequence in context: A028938 A038213 A261207 * A270598 A001579 A327871

Adjacent sequences: A161936 A161937 A161938 * A161940 A161941 A161942

Keyword

nonn

Author

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

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

Status

approved