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A137879
Numbers k such that k^2 is a 17-gonal number.
4
1, 133, 615, 64107, 296429, 30899441, 142878163, 14893466455, 68866978137, 7178619931869, 33193740583871, 3460079913694403, 15999314094447685, 1667751339780770377, 7711636199783200299, 803852685694417627311, 3716992648981408096433
OFFSET
1,2
COMMENTS
Corresponding 17-gonal numbers equal k^2 are listed in A137878.
The 17-gonal numbers A051869(n) = n*(15n - 13)/2 are perfect squares for indices n listed in A137880. Note that all such indices are also perfect squares of numbers listed in A137881.
FORMULA
a(n) = sqrt(A137878(n)) = sqrt(A051869(A137880(n))) = sqrt(A051869(A137881(n)^2)).
From Max Alekseyev, Oct 19 2008: (Start)
For n>=5, a(n) = 482*a(n-2) - a(n-4).
a(2n) = (-60 + 17*sqrt(30))/120 * (11 + 2*sqrt(30))^(2n) + (-60 - 17*sqrt(30))/120 * (11 - 2*sqrt(30))^(2n).
a(2n+1) = (60 + 17*sqrt(30))/120 * (11 + 2*sqrt(30))^(2n) + (60 - 17*sqrt(30))/120 * (11 - 2*sqrt(30))^(2n). (End)
MATHEMATICA
LinearRecurrence[{0, 482, 0, -1}, {1, 133, 615, 64107}, 20] (* Harvey P. Dale, May 12 2014 *)
PROG
(PARI) is(n)=ispolygonal(n^2, 17) \\ Charles R Greathouse IV, Oct 16 2015
CROSSREFS
Cf. A051869 (17-gonal numbers), A137878 (17-gonal numbers that are perfect squares), A137880, A137881.
Sequence in context: A251131 A267288 A334037 * A249108 A020237 A217690
KEYWORD
nonn,easy
AUTHOR
Alexander Adamchuk, Feb 19 2008
EXTENSIONS
Extended by Max Alekseyev, Oct 19 2008
STATUS
approved