The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

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