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
Links
- Colin Barker, Table of n, a(n) for n = 0..394
- Index entries for linear recurrences with constant coefficients, signature (340,-1).
Programs
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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
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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);
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Mathematica
LinearRecurrence[{340, -1}, {66, 22335}, 20] (* Bruno Berselli, Nov 17 2015 *) -
PARI
Vec(-3*(35*x-22)/(x^2-340*x+1) + O(x^20)) \\ Colin Barker, Nov 16 2015
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
Extensions
Definition corrected by Richard Choulet, Nov 15 2009
Typo in title fixed by Colin Barker, Nov 16 2015