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A137880
Indices k of perfect squares among 17-gonal numbers A051869(k) = k*(15*k - 13)/2.
4
1, 49, 225, 23409, 108241, 11282881, 52171729, 5438325025, 25146664929, 2621261378961, 12120640323841, 1263442546333969, 5842123489426225, 608976686071593889, 2815891401263116401, 293525499243961920321, 1357253813285332678849, 141478681658903574000625
OFFSET
1,2
COMMENTS
Corresponding perfect squares are listed in A137878.
Note that all a(n) are perfect squares themselves, their square roots are listed in A137881.
FORMULA
A051869( a(n) ) = A137878(n); a(n) = A137881(n)^2.
From Max Alekseyev, Oct 19 2008: (Start)
a(n) = 482*a(n-2) - a(n-4) - 208.
a(2n) = ( (15 - sqrt(30))/30 * (11 + 2*sqrt(30))^n + (15 + sqrt(30))/30 * (11 - 2*sqrt(30))^n )^2.
a(2n+1) = ( (15 + sqrt(30))/30 * (11 + 2*sqrt(30))^n + (15 - sqrt(30))/30 * (11 - 2*sqrt(30))^n )^2. (End)
a(n) = a(n-1) + 482*a(n-2) - 482*a(n-3) - a(n-4) + a(n-5). - Matthew House, Jun 18 2016
G.f.: x*(1 + 48*x - 306*x^2 + 48*x^3 + x^4) / ((1-x)*(1 - 22*x + x^2)*(1 + 22*x + x^2)). - Colin Barker, Jun 18 2016
MATHEMATICA
Rest@ CoefficientList[Series[x (1 + 48 x - 306 x^2 + 48 x^3 + x^4)/((1 - x) (1 - 22 x + x^2) (1 + 22 x + x^2)), {x, 0, 18}], x] (* Michael De Vlieger, Jun 18 2016 *)
PROG
(PARI) Vec(x*(1+48*x-306*x^2+48*x^3+x^4)/((1-x)*(1-22*x+x^2)*(1+22*x+x^2)) + O(x^20)) \\ Colin Barker, Jun 18 2016
CROSSREFS
Cf. A051869 (17-gonal numbers), A137878 (17-gonal numbers that are perfect squares), A137879, A137881.
Sequence in context: A192359 A100453 A017150 * A264538 A266799 A211741
KEYWORD
nonn,easy
AUTHOR
Alexander Adamchuk, Feb 19 2008
EXTENSIONS
Edited and extended by Max Alekseyev, Oct 19 2008
STATUS
approved