OFFSET
1,2
COMMENTS
LINKS
Colin Barker, Table of n, a(n) for n = 1..746
Giovanni Lucca, Circle Chains Inscribed in Symmetrical Lenses and Integer Sequences, Forum Geometricorum, Volume 16 (2016) 419-427.
Index entries for linear recurrences with constant coefficients, signature (23,-23,1).
FORMULA
a(n) = 23*a(n-1)-23*a(n-2)+a(n-3).
G.f.: -x*(x^2-12*x+1) / ((x-1)*(x^2-22*x+1)).
a(n) = 1/2+1/24*(11+2*sqrt(30))^(-n)*(6+sqrt(30)-(-6+sqrt(30))*(11+2*sqrt(30))^(2*n)). - Colin Barker, Mar 03 2016
EXAMPLE
11 is in the sequence because the 11th centered hexagonal number is 331, which is also the 12th centered pentagonal number.
MATHEMATICA
LinearRecurrence[{23, -23, 1}, {1, 11, 231}, 20] (* Harvey P. Dale, Mar 01 2022 *)
PROG
(PARI) Vec(-x*(x^2-12*x+1)/((x-1)*(x^2-22*x+1)) + O(x^100))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Feb 07 2015
STATUS
approved