OFFSET
1,2
COMMENTS
A137880 gives the indices m (= a(n)^2) of perfect squares in 17-gonal numbers A051869(m) = m(15m -13)/2. Corresponding 17-gonal numbers are listed in A137878(n) = A051869( a(n)^2 ).
Positive values of x (or y) satisfying x^2 - 22xy + y^2 + 104 = 0. - Colin Barker, Feb 19 2014
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..200
Index entries for linear recurrences with constant coefficients, signature (0,22,0,-1).
FORMULA
For n>=5, a(n) = 22*a(n-2) - a(n-4). [Alekseyev]
a(2n) = (15 - sqrt(30))/30 * (11 + 2*sqrt(30))^n + (15 + sqrt(30))/30 * (11 - 2*sqrt(30))^n. [Alekseyev]
a(2n+1) = (15 + sqrt(30))/30 * (11 + 2*sqrt(30))^n + (15 - sqrt(30))/30 * (11 - 2*sqrt(30))^n. [Alekseyev]
G.f.: -x*(x-1)*(x^2+8*x+1) / (x^4-22*x^2+1). - Colin Barker, Feb 19 2014
MATHEMATICA
CoefficientList[Series[(1 - x) (x^2 + 8 x + 1)/(x^4 - 22 x^2 + 1), {x, 0, 40}], x] (* Vincenzo Librandi, Feb 21 2014 *)
PROG
(Magma) I:=[1, 7, 15, 153]; [n le 4 select I[n] else 22*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Feb 21 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alexander Adamchuk, Feb 19 2008
EXTENSIONS
Edited and extended by Max Alekseyev, Oct 19 2008
STATUS
approved