OFFSET
1,3
LINKS
Nathaniel Johnston, Table of n, a(n) for n = 1..500
Index entries for linear recurrences with constant coefficients, signature (5,10).
FORMULA
a(n) = ((5+sqrt(65))^(n-1) - (5-sqrt(65))^(n-1))/(2^(n-1)*sqrt(65)). - Rolf Pleisch, May 14 2011
G.f.: x^2/(1-5*x-10*x^2).
a(n) = (i*sqrt(10))^(n-1) * ChebyshevU(n-1, -i*sqrt(5/8)). - G. C. Greubel, Jul 21 2023
MATHEMATICA
Join[{a=0, b=1}, Table[c=5*b+10*a; a=b; b=c, {n, 100}]]
LinearRecurrence[{5, 10}, {0, 1}, 30] (* G. C. Greubel, Jan 16 2018 *)
PROG
(PARI) a(n)=([0, 1; 10, 5]^(n-1))[1, 2] \\ Charles R Greathouse IV, Oct 03 2016
(PARI) my(x='x+O('x^30)); concat([0], Vec(x^2/(1-5*x-10*x^2))) \\ G. C. Greubel, Jan 16 2018
(Magma) [n le 2 select n-1 else 5*Self(n-1) +10*Self(n-2): n in [1..30]]; // G. C. Greubel, Jan 16 2018
(SageMath)
A180250= BinaryRecurrenceSequence(5, 10, 0, 1)
[A180250(n-1) for n in range(1, 41)] # G. C. Greubel, Jul 21 2023
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, A030195, A053404, A057087, A057088, A083858, A085939, A090017, A091914, A099012, A180222, A180226.
KEYWORD
nonn,easy
AUTHOR
Vladimir Joseph Stephan Orlovsky, Jan 16 2011
STATUS
approved