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