OFFSET
0,1
COMMENTS
Third binomial transform of A162396.
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (6, -7).
FORMULA
a(n) = 6*a(n-1) - 7*a(n-2) for n > 1; a(0) = 5, a(1) = 17.
G.f.: (5-13*x)/(1-6*x+7*x^2).
MAPLE
seq(coeff(series((5-13*x)/(1-6*x+7*x^2), x, n+1), x, n), n = 0..25); # Muniru A Asiru, Sep 28 2018
MATHEMATICA
LinearRecurrence[{6, -7}, {5, 17}, 30] (* Harvey P. Dale, Jun 04 2016 *)
PROG
(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((5+r)*(3+r)^n+(5-r)*(3-r)^n)/2: n in [0..23] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 02 2009
(Magma) I:=[5, 17]; [n le 2 select I[n] else 6*Self(n-1) - 7*Self(n-2): n in [1..30]]; // G. C. Greubel, Sep 28 2018
(PARI) x='x+O('x^30); Vec((5-13*x)/(1-6*x+7*x^2)) \\ G. C. Greubel, Sep 28 2018
(GAP) a:=[5, 17];; for n in [3..25] do a[n]:=6*a[n-1]-7*a[n-2]; od; a; # Muniru A Asiru, Sep 28 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Jun 29 2009
EXTENSIONS
Edited and extended beyond a(5) by Klaus Brockhaus, Jul 02 2009
STATUS
approved
