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A137881 a(n) = sqrt(A137880(n)). 5
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 (list; graph; refs; listen; history; text; internal format)
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
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
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
Cf. A051869 (17-gonal numbers), A137878 (17-gonal numbers that are perfect squares), A137879, A137880.
Sequence in context: A243470 A068366 A156499 * A042725 A041096 A248275
KEYWORD
nonn,easy
AUTHOR
Alexander Adamchuk, Feb 19 2008
EXTENSIONS
Edited and extended by Max Alekseyev, Oct 19 2008
STATUS
approved

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Last modified April 22 18:29 EDT 2024. Contains 371906 sequences. (Running on oeis4.)