A137881 a(n) = sqrt(A137880(n)).

1, 7, 15, 153, 329, 3359, 7223, 73745, 158577, 1619031, 3481471, 35544937, 76433785, 780369583, 1678061799, 17132585889, 36840925793, 376136519975, 808822305647, 8257870853561, 17757249798441, 181297022258367, 389850673260055, 3980276618830513, 8558957561922769

Offset: 1

Author

Alexander Adamchuk, Feb 19 2008

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A051869 (17-gonal numbers), A137878 (17-gonal numbers that are perfect squares), A137879, A137880.

Programs

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

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 *)

Formula

a(n) = sqrt(A137880(n)). A051869( a(n)^2 ) = A137878(n).

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

Extensions

Edited and extended by Max Alekseyev, Oct 19 2008