A167780 Subsequence of A167708 whose indices are 0 mod 5, that is, a(n) = A167708(5n+5).
959, 326050, 110856041, 37690727890, 12814736626559, 4356972762302170, 1481357924446111241, 503657337338915519770, 171242013337306830610559, 58221780877346983492070290, 19795234256284637080473288041
Offset: 0
Examples
a(0) = A167708(5) = 959, a(1) = A167708(10) = 326050,...
Links
- Index entries for linear recurrences with constant coefficients, signature (340, -1).
Programs
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Maple
u(0):=959:u(1):=326050:for n from 0 to 20 do u(n+2):=340*u(n+1)-u(n):od:seq(u(n),n=0..20); taylor(((959+326050*z-959*z*340)/(1-340*z+z^2)),z=0,20); for n from 0 to 20 do u(n):=simplify((220*sqrt(19)+959)/2*(170+39*sqrt(19))^(n)+(-220*sqrt(19)+959)/2*(170-39*sqrt(19))^(n)):od:seq(u(n),n=0..20);
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Mathematica
LinearRecurrence[{340,-1}, {959,326050}, 20] (* Harvey P. Dale, Aug 06 2013 *)
Formula
a(n+2) = 340*a(n+1) - a(n).
a(n+1) = 170*a(n) + 39*sqrt(19*a(n)^2 - 1539).
G.f.: (959 - 10*z)/(1 - 340*z + z^2).
a(n) = (220*sqrt(19) + 959)/2*(170 + 39*sqrt(19))^n + (-220*sqrt(19) + 959)/2*(170 - 39*sqrt(19))^n. - Richard Choulet, Nov 13 2009
a(n) = 10*cosh(x*log(170 + 39*Sqrt[19])) - Sqrt[19]*sinh(x*log(170 + 39*Sqrt[19])). - Harvey P. Dale, Aug 06 2013