A167820 Subsequence of A167709 whose indices are congruent to 0 mod 5, i.e., a(n) = A167709(5*n).

0, 351, 119340, 40575249, 13795465320, 4690417633551, 1594728199942020, 542202897562653249, 184347390443102162640, 62677570547757172644351, 21310189638846995596916700, 7245401799637430745779033649, 2463415301687087606569274523960

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

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.: 351*z/(1 - 340*z + z^2).

a(n) = (9*sqrt(19))/38*(170 + 39*sqrt(19))^n + (-9*sqrt(19))/38*(170 - 39*sqrt(19))^n.

Example

a(0)=0 because a(0) = A167709(0) = 0, a(1)=351 because a(1) = A167709(5) = 351.

Maple

w(0):=0: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((9*sqrt(19))/38*(170+39*sqrt(19))^(n)+(-9*sqrt(19))/38*(170-39*sqrt(19))^(n)):od:seq(u(n), n=0..20); taylor(((351*z)/(1-340*z+z^2)), z=0, 21); A167709

Mathematica

RecurrenceTable[{a[1] == 0, a[2] == 351, a[n] == 340 a[n-1] - a[n-2]}, a, {n, 30}] (* Vincenzo Librandi, Jun 28 2016 *)
LinearRecurrence[{340, -1}, {0, 351}, 20] (* Harvey P. Dale, Dec 25 2018 *)

Prog

(Magma) I:=[0, 351]; [n le 2 select I[n] else 340*Self(n-1)-Self(n-2): n in [1..30]]; // Vincenzo Librandi, Jun 28 2016

Crossrefs

Cf. A167709.

Sequence in context: A220333 A221294 A220686 * A145633 A252250 A235888

Adjacent sequences: A167817 A167818 A167819 * A167821 A167822 A167823

Keyword

easy,nonn

Author

Richard Choulet, Nov 13 2009

Status

approved