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A171640 a(n) = 10*a(n-1)-a(n-2)-4 with a(1)=1 and a(2)=3. 1
1, 3, 25, 243, 2401, 23763, 235225, 2328483, 23049601, 228167523, 2258625625, 22358088723, 221322261601, 2190864527283, 21687323011225, 214682365584963, 2125136332838401, 21036680962799043, 208241673295152025, 2061380051988721203, 20405558846592060001 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

Giovanni Lucca, Integer Sequences and Circle Chains Inside a Circular Segment, Forum Geometricorum, Vol. 18 (2018), 47-55.

Index entries for linear recurrences with constant coefficients, signature (11,-11,1).

FORMULA

a(n)= A132596(n-1)+1.

2*a(n)+ 2*A132596(n-1) = A087799(n-1).

a(n+1) = [(sqrt(3)-sqrt(2))^n +(sqrt(3)+ sqrt(2))^n]^2 / 4.

From Colin Barker, Oct 02 2015: (Start)

a(n) = 11*a(n-1) - 11*a(n-2) + a(n-3) for n>3.

G.f.: -x*(3*x^2-8*x+1) / ((x-1)*(x^2-10*x+1)).

(End)

6*a(n)*(a(n)-1) = [A122653(n-1)]^2. - Jean-Luc Manguin, Jun 02 2020

EXAMPLE

a(2+1) = [5-sqrt(24)+5+sqrt(24)]^2/4 = 100/4 = 25.

MATHEMATICA

RecurrenceTable[{a[n] == 10 a[n - 1] - a[n - 2] - 4, a[1] == 1, a[2] == 3}, a, {n, 1, 21}] (* Michael De Vlieger, Oct 02 2015 *)

LinearRecurrence[{11, -11, 1}, {1, 3, 25}, 30] (* Harvey P. Dale, May 05 2018 *)

PROG

(PARI) Vec(-x*(3*x^2-8*x+1)/((x-1)*(x^2-10*x+1)) + O(x^30)) \\ Colin Barker, Oct 02 2015

CROSSREFS

Cf. A132596, A087799, A001263.

Sequence in context: A332468 A134272 A335117 * A099913 A245925 A260209

Adjacent sequences:  A171637 A171638 A171639 * A171641 A171642 A171643

KEYWORD

nonn,easy

AUTHOR

Mark Dols, Dec 13 2009

STATUS

approved

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Last modified September 24 17:09 EDT 2020. Contains 337321 sequences. (Running on oeis4.)