OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (14, -44).
FORMULA
From Philippe Deléham, Nov 26 2008: (Start)
a(n) = 14*a(n-1) - 44*a(n-2), n > 1; a(0)=1, a(1)=7.
G.f.: (1-7*x)/(1-14*x+44*x^2).
a(n) = (Sum_{k=0..n} A098158(n,k)*7^(2*k)*5^(n-k))/7^n. (End)
MATHEMATICA
With[{srt5=Sqrt[5]}, Simplify/@Table[((7+srt5)^n+(7-srt5)^n)/2, {n, 0, 20}]] (* or *) LinearRecurrence[{14, -44}, {1, 7}, 20] (* Harvey P. Dale, Jan 16 2012 *)
CoefficientList[Series[(1 - 7 x) / (1 - 14 x + 44 x^2), {x, 0, 40}], x] (* Vincenzo Librandi, Feb 04 2018 *)
PROG
(Magma) Z<x>:= PolynomialRing(Integers()); N<r5>:=NumberField(x^2-5); S:=[ ((7+r5)^n+(7-r5)^n)/2: n in [0..18] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Nov 26 2008
(Magma) I:=[1, 7]; [n le 2 select I[n] else 14*Self(n-1)-44*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Feb 04 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Nov 24 2008
EXTENSIONS
Extended beyond a(6) by Klaus Brockhaus, Nov 26 2008
STATUS
approved