A161940 a(n) = ((3+sqrt(2))*(5+sqrt(2))^n + (3-sqrt(2))*(5-sqrt(2))^n)/2.

3, 17, 101, 619, 3867, 24433, 155389, 991931, 6345363, 40639217, 260448821, 1669786219, 10707539307, 68670310033, 440429696269, 2824879831931, 18118915305123, 116216916916817, 745434117150341, 4781352082416619

Offset

0,1

Comments

Fifth binomial transform of A162255.

Links

Muniru A Asiru, Table of n, a(n) for n = 0..256

Index entries for linear recurrences with constant coefficients, signature (10, -23).

Formula

a(n) = 10*a(n-1) - 23*a(n-2) for n > 1; a(0) = 3, a(1) = 17.

G.f.: (3-13*x)/(1-10*x+23*x^2).

Maple

a[0] := 3: a[1] := 17: for n from 2 to 20 do a[n] := 10*a[n-1]-23*a[n-2] end do: seq(a[n], n = 0 .. 20); # Emeric Deutsch, Jun 27 2009

Mathematica

LinearRecurrence[{10, -23}, {3, 17}, 30] (* Harvey P. Dale, Oct 05 2012 *)

Prog

(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((3+r)*(5+r)^n+(3-r)*(5-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 01 2009
(GAP) a := [3, 17];; for n in [3..10^2] do a[n] := 10*a[n-1] - 23*a[n-2]; od; a; # Muniru A Asiru, Feb 02 2018
(PARI) x='x+O('x^30); Vec((3-13*x)/(1-10*x+23*x^2)) \\ G. C. Greubel, Aug 17 2018

Crossrefs

Cf. A162255, A161939 (fourth binomial transform of A162255).

Sequence in context: A322242 A356392 A330626 * A074565 A339565 A241768

Adjacent sequences: A161937 A161938 A161939 * A161941 A161942 A161943

Keyword

nonn

Author

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

Extensions

Edited and extended beyond a(4) by Klaus Brockhaus, Jul 01 2009

Extended by Emeric Deutsch, Jun 27 2009

Status

approved