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A167778
Subsequence of A167708 whose indices are 2 mod 5.
7
66, 22335, 7593834, 2581881225, 877832022666, 298460305825215, 101475626148550434, 34501414430201322345, 11730379430642301046866, 3988294505003952154612095, 1356008401321913090267065434, 461038868154945446738647635465, 156751859164280129978049928992666
OFFSET
0,1
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
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