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

Author

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

Keywords

• nonn

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).

Crossrefs

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

Programs

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

Magma

Z:=PolynomialRing(Integers()); N:=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

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 *)

PARI

x='x+O('x^30); Vec((3-13*x)/(1-10*x+23*x^2)) \\ G. C. Greubel, Aug 17 2018

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).

Extensions

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

Extended by Emeric Deutsch, Jun 27 2009