A167775 Subsequence of A167708 whose indices are congruent to 1 mod 5, i.e., a(n) = A167708(5n+1).

10, 2441, 829930, 282173759, 95938248130, 32618722190441, 11090269606501810, 3770659047488424959, 1282012985876457984250, 435880644538948226220041, 148198137130256520456829690, 50386930743642678007095874559, 17131408254701380265892140520370

Offset: 0

Author

Richard Choulet, Nov 11 2009

Keywords

• easy
• nonn
• changed

Comments

Solutions to the Pell equation a(n)^2 - 19*b(n)^2 = 81. The corresponding b(n) are in A167822. - Klaus Purath, Aug 31 2025

Examples

			a(0) = A167708(1) = 10, a(1) = A167708(6) = 2441, ...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..250
• Index entries for linear recurrences with constant coefficients, signature (340,-1).

Crossrefs

Cf. A167708, A167709, A167774, A167778, A167779, A167780, A167822.

Programs

Magma

I:=[10,2441]; [n le 2 select I[n] else 340*Self(n-1)-Self(n-2): n in [1..20]]; // Vincenzo Librandi, Jun 24 2016

Maple

u(0):=10:u(1):=2441:for n from 0 to 20 do u(n+2):=340*u(n+1)-u(n):od:seq(u(n),n=0..20); taylor(((10+2441*z-10*z*340)/(1-340*z+z^2)),z=0,20);

Mathematica

LinearRecurrence[{340, -1}, {10, 2441}, 50] (* G. C. Greubel, Jun 23 2016 *)

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.: (10 + 2441*z - 10*z*340)/(1 - 340*z + z^2).

a(n) = ((10 + sqrt(19))/2)*(170 + 39*sqrt(19))^(n) + ((10 - sqrt(19))/2)* (170 - 39*sqrt(19))^(n).