A180250 a(n) = 5*a(n-1) + 10*a(n-2), with a(1)=0 and a(2)=1.

0, 1, 5, 35, 225, 1475, 9625, 62875, 410625, 2681875, 17515625, 114396875, 747140625, 4879671875, 31869765625, 208145546875, 1359425390625, 8878582421875, 57987166015625, 378721654296875, 2473479931640625, 16154616201171875, 105507880322265625

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.

Sequence in context: A221578 A320071 A024062 * A002074 A187444 A166176

Adjacent sequences: A180247 A180248 A180249 * A180251 A180252 A180253

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Jan 16 2011

Status

approved