A167825 Subsequence of A167709 whose indices are congruent to 4 mod 5, i.e., a(n) = A167709(5*n+4).

220, 74801, 25432120, 8646845999, 2939902207540, 999558103717601, 339846815361776800, 115546917664900394399, 39285612159250772318860, 13356992587227597688018001, 4541338194045223963153801480

Offset

0,1

Links

G. C. Greubel, Table of n, a(n) for n = 0..100

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

Formula

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

a(n+1) = 170*a(n) + 39*sqrt(19*(w(n))^2 + 81).

G.f.: (220 + x)/(1 - 340*x + x^2).

a(n) = ((959*sqrt(19) + 4180)/38)*(170 + 39*sqrt(19))^n + ((-959*sqrt(19) + 4180)/38)*(170 - 39*sqrt(19))^n.

Example

a(0) = A167709(4) = 220, a(1) = A167709(9) = 74801.

Maple

w(0):=220:for n from 0 to 20 do w(n+1):=170*w(n)+39*sqrt(19*(w(n))^2+81) :od: seq(w(n), n=0..20); for n from 0 to 20 do u(n):=simplify((959*sqrt(19)+4180)/38*(170+39*sqrt(19))^(n)+(-959*sqrt(19)+4180)/38*(170-39*sqrt(19))^(n)):od:seq(u(n), n=0..20); taylor(((220+74801*z-220*340*z)/(1-340*z+z^2)), z=0, 21);

Mathematica

LinearRecurrence[{340, -1}, {220, 74801}, 50] (* G. C. Greubel, Jun 27 2016 *)
RecurrenceTable[{a[1] == 220, a[2] == 74801, a[n] == 340 a[n-1] - a[n-2]}, a, {n, 15}] (* Vincenzo Librandi, Jun 28 2016 *)

Prog

(Magma) I:=[220, 74801]; [n le 2 select I[n] else 340*Self(n-1)-Self(n-2): n in [1..30]]; // Vincenzo Librandi, Jun 28 2016

Crossrefs

Sequence in context: A049023 A282591 A091756 * A339680 A266237 A371899

Adjacent sequences: A167822 A167823 A167824 * A167826 A167827 A167828

Keyword

nonn,easy

Author

Richard Choulet, Nov 13 2009

Status

approved