OFFSET
0,3
COMMENTS
Let the generator matrix for the ternary Golay G_12 code be [I|B], where the elements of B are taken from the set {0,1,2}. Then a(n)=(B^n)_1,2 for instance. - Paul Barry, Feb 13 2004
Pisano period lengths: 1, 2, 4, 4, 1, 4, 42, 8, 12, 2, 10, 4, 12, 42, 4, 16, 96, 12, 360, 4, ... - R. J. Mathar, Aug 10 2012
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Lucyna Trojnar-Spelina, Iwona Włoch, On Generalized Pell and Pell-Lucas Numbers, Iranian Journal of Science and Technology, Transactions A: Science (2019), 1-7.
Index entries for linear recurrences with constant coefficients, signature (6,5).
FORMULA
a(n) = 6*a(n-1) + 5*a(n-2).
a(n) = sqrt(14)*(3+sqrt(14))^n/28 - sqrt(14)*(3-sqrt(14))^n/28. - Paul Barry, Feb 13 2004
MATHEMATICA
Join[{a=0, b=1}, Table[c=6*b+5*a; a=b; b=c, {n, 100}]] (* Vladimir Joseph Stephan Orlovsky, Jan 16 2011 *)
CoefficientList[Series[x/(1-6x-5x^2), {x, 0, 20}], x] (* or *) LinearRecurrence[ {6, 5}, {0, 1}, 30] (* Harvey P. Dale, Oct 30 2017 *)
PROG
(Sage) [lucas_number1(n, 6, -5) for n in range(0, 21)] # Zerinvary Lajos, Apr 24 2009
(Magma) I:=[0, 1]; [n le 2 select I[n] else 6*Self(n-1)+5*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 14 2011
(PARI) a(n)=([0, 1; 5, 6]^n*[0; 1])[1, 1] \\ Charles R Greathouse IV, Oct 03 2016
CROSSREFS
Cf. A001076, A006190, A007482, A015520, A015521, A015523, A015524, A015525, A015528, A015529, A015530, A015531, A015532, A015533, A015534, A015535, A015536, A015537, A015440, A015441, A015443, A015444, A015445, A015447, A015548, A030195, A053404, A057087, A057088, A057089, A083858, A085939, A090017, A091914, A099012, A135030, A135032, A180222, A180226, A180250.
KEYWORD
nonn,easy
AUTHOR
STATUS
approved