OFFSET
0,3
COMMENTS
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (7,-7,1).
FORMULA
a(n) = 6*a(n-1) - a(n-2) + 12.
a(0)=-1, a(1)=1, a(2)=19, a(n) = 7*a(n-1) - 7*a(n-2) + a(n-3). - Harvey P. Dale, Feb 09 2014
From Colin Barker, Mar 05 2016: (Start)
a(n) = -3 + (1/4)*( (4-sqrt(2))*(3+2*sqrt(2))^n + (4+sqrt(2))*(3-2*sqrt(2))^n ).
G.f.: -(1-8*x-5*x^2) / ((1-x)*(1-6*x+x^2)).
(End)
MAPLE
Pell:= proc(n) option remember;
if n<2 then n
else 2*Pell(n-1) + Pell(n-2)
fi; end:
seq(Pell(2*n) + 2*Pell(2*n-1) - 3, n=0..40); # G. C. Greubel, May 24 2021
MATHEMATICA
LinearRecurrence[{7, -7, 1}, {-1, 1, 19}, 30] (* Harvey P. Dale, Feb 09 2014 *)
PROG
(Magma) I:=[-1, 1]; [n le 2 select I[n] else 6*Self(n-1)-Self(n-2)+12: n in [1..30]]; // Vincenzo Librandi, Feb 10 2014
(PARI) Vec(-(1-8*x-5*x^2)/((1-x)*(1-6*x+x^2)) + O(x^30)) \\ Colin Barker, Mar 05 2016
(Sage) [lucas_number2(2*n, 2, -1) - lucas_number1(2*n, 2, -1) - 3 for n in (0..40)] # G. C. Greubel, May 24 2021
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Kenneth J Ramsey, Apr 17 2012
EXTENSIONS
More terms from Harvey P. Dale, Feb 09 2014
STATUS
approved