A167824 Subsequence of A167709 whose indices are congruent to 3 mod 5, i.e., a(n) = A167709(5*n+3).

24, 8175, 2779476, 945013665, 321301866624, 109241689638495, 37141853175221676, 12628120837885731345, 4293523943027973435624, 1459785512508673082380815, 496322780729005820036041476, 168748285662349470139171721025

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.: (24 + 15*x)/(1 - 340*x + x^2).

a(n) = ((105*sqrt(19) + 456)/38)*(170 + 39*sqrt(19))^n + ((-105*sqrt(19) + 456)/38)*(170 - 39*sqrt(19))^n.

Example

a(0) = A167709(3) = 24, a(1) = A167709(8) = 8175.

Maple

w(0):=24: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((105*sqrt(19)+456)/38*(170+39*sqrt(19))^(n)+(-105*sqrt(19)+456)/38*(170-39*sqrt(19))^(n)):od:seq(u(n), n=0..20); taylor(((24+8175*z-24*340*z)/(1-340*z+z^2)), z=0, 21);

Mathematica

LinearRecurrence[{340, -1}, {24, 8175}, 50] (* G. C. Greubel, Jun 27 2016 *)
RecurrenceTable[{a[1] == 24, a[2] == 8175, a[n] == 340*a[n-1] -a[n-2]}, a, {n, 15}] (* Vincenzo Librandi, Jun 28 2016 *)

Prog

(Magma) I:=[24, 8175]; [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: A297049 A147860 A159409 * A266658 A065142 A233148

Adjacent sequences: A167821 A167822 A167823 * A167825 A167826 A167827

Keyword

nonn,easy

Author

Richard Choulet, Nov 13 2009

Status

approved