A167778 Subsequence of A167708 whose indices are 2 mod 5.

66, 22335, 7593834, 2581881225, 877832022666, 298460305825215, 101475626148550434, 34501414430201322345, 11730379430642301046866, 3988294505003952154612095, 1356008401321913090267065434, 461038868154945446738647635465, 156751859164280129978049928992666

Offset

0,1

Links

Colin Barker, Table of n, a(n) for n = 0..394

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

Formula

a(n) = A167708(5n+2).

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

a(n+1) = 170*a(n) + 39*sqrt(19*a(n)^2-1539).

G.f.: (66 + 22335*x - 66*x*340)/(1 - 340*x + x^2).

a(n) = ((66 + 15*sqrt(19))/2)*(170 + 39*sqrt(19))^n + ((66 - 15*sqrt(19)) /2)*(170 - 39*sqrt(19))^n. - Richard Choulet, Nov 13 2009

G.f.: -3*(35*x - 22) / (x^2 - 340*x + 1). - Colin Barker, Nov 16 2015

Maple

u(0):=66:u(1):=22335:for n from 0 to 20 do u(n+2):=340*u(n+1)-u(n):od:seq(u(n), n=0..20); taylor(((66+22335*z-66*z*340)/(1-340*z+z^2)), z=0, 20); for n from 0 to 20 do u(n):=simplify((15*sqrt(19)+66)/2*(170+39*sqrt(19))^(n)+(-15*sqrt(19)+66)/2*(170-39*sqrt(19))^(n)):od:seq(u(n), n=0..20);

Mathematica

LinearRecurrence[{340, -1}, {66, 22335}, 20] (* Bruno Berselli, Nov 17 2015 *)

Prog

(PARI) Vec(-3*(35*x-22)/(x^2-340*x+1) + O(x^20)) \\ Colin Barker, Nov 16 2015
(Magma) I:=[66, 22335]; [n le 2 select I[n] else 340*Self(n-1)-Self(n-2): n in [1..20]]; // Vincenzo Librandi, Nov 17 2015

Crossrefs

Cf. A167708, A167709, A167774, A167775, A167779, A167780. - Richard Choulet, Nov 11 2009

Sequence in context: A127706 A355470 A356688 * A199838 A188453 A278848

Adjacent sequences: A167775 A167776 A167777 * A167779 A167780 A167781

Keyword

nonn,easy

Author

Richard Choulet, Nov 11 2009

Extensions

Definition corrected by Richard Choulet, Nov 15 2009

Typo in title fixed by Colin Barker, Nov 16 2015

Status

approved