A167823 Subsequence of A167709 whose indices are congruent to 2 mod 5, i.e., a(n) = A167709(5*n+2).

15, 5124, 1742145, 592324176, 201388477695, 68471490092124, 23280105242844465, 7915167311077025976, 2691133605660945987375, 914977510757410558681524, 311089662523913929005730785, 105769570280619978451389785376, 35961342805748268759543521297055

Offset

0,1

Links

G. C. Greubel, Table of n, a(n) for n = 0..100

Index entries for linear recurrences with constant coefficients, signature (340,-1).

Formula

a(n+2) = 340*a(n+1) - a(n).

a(n+1) = 170*a(n) + 39*sqrt(19*(a(n))^2 + 81).

G.f.: (15 + 24*z)/(1 - 340*z + z^2).

a(n) = (66*sqrt(19) + 285)/38*(170 + 39*sqrt(19))^n + (-66*sqrt(19) + 285)/38*(170 - 39*sqrt(19))^n.

Example

a(0) = A167709(2) = 15, a(1) = A167709(7) = 5124.

Maple

w(0):=15:for n from 0 to 20 do w(n+1):=170*w(n)+39*sqrt(19*(w(n))^2+81) :od: seq(w(n), n=0..20); for n from 0 to 20 do u(n):=simplify((66*sqrt(19)+285)/38*(170+39*sqrt(19))^(n)+(-66*sqrt(19)+285)/38*(170-39*sqrt(19))^(n)):od:seq(u(n), n=0..20); taylor(((15+5124*z-15*340*z)/(1-340*z+z^2)), z=0, 21);

Mathematica

LinearRecurrence[{340, -1}, {15, 5124}, 50] (* G. C. Greubel, Jun 27 2016 *)
RecurrenceTable[{a[1] == 15, a[2] == 5124, a[n] == 340 a[n-1] - a[n-2]}, a, {n, 15}] (* Vincenzo Librandi, Jun 28 2016 *)

Prog

(Magma) I:=[15, 5124]; [n le 2 select I[n] else 340*Self(n-1)-Self(n-2): n in [1..30]]; // Vincenzo Librandi, Jun 28 2016

Crossrefs

Sequence in context: A206387 A198903 A249966 * A199099 A251820 A296177

Adjacent sequences: A167820 A167821 A167822 * A167824 A167825 A167826

Keyword

easy,nonn

Author

Richard Choulet, Nov 13 2009

Status

approved